Quanquan Gu

TMLR Journal 2026 Journal Article

Multi-Step Alignment as Markov Games: An Optimistic Online Mirror Descent Approach with Convergence Guarantees

• Yongtao Wu
• Luca Viano
• Kimon Antonakopoulos
• Yihang Chen
• Zhenyu Zhu
• Quanquan Gu
• Volkan Cevher

Reinforcement Learning from Human Feedback (RLHF) has been highly successful in aligning large language models with human preferences. While prevalent methods like DPO have demonstrated strong performance, they frame interactions with the language model as a bandit problem, which limits their applicability in real-world scenarios where multi-turn conversations are common. Additionally, DPO relies on the Bradley-Terry model assumption, which does not adequately capture the non-transitive nature of human preferences. In this paper, we address these challenges by modeling the alignment problem as a two-player constant-sum Markov game, where each player seeks to maximize their winning rate against the other across all steps of the conversation. Our approach Optimistic Multi-step Preference Optimization (OMPO) is built upon the optimistic online mirror descent algorithm~\citep{rakhlin2013online,joulani17a}. Theoretically, we provide a rigorous analysis for the convergence of OMPO and show that OMPO requires $\mathcal{O}(\epsilon^{-1})$ policy updates to converge to an $\epsilon$-approximate Nash equilibrium. We also validate the effectiveness of our method on multi-turn conversations dataset and math reasoning dataset.

ICML Conference 2025 Conference Paper

An All-Atom Generative Model for Designing Protein Complexes

• Ruizhe Chen
• Dongyu Xue
• Xiangxin Zhou
• Zaixiang Zheng
• Xiangxiang Zeng
• Quanquan Gu

Proteins typically exist in complexes, interacting with other proteins or biomolecules to perform their specific biological roles. Research on single-chain protein modeling has been extensively and deeply explored, with advancements seen in models like the series of ESM and AlphaFold2. Despite these developments, the study and modeling of multi-chain proteins remain largely uncharted, though they are vital for understanding biological functions. Recognizing the importance of these interactions, we introduce APM (all-Atom Protein generative Model), a model specifically designed for modeling multi-chain proteins. By integrating atom-level information and leveraging data on multi-chain proteins, APM is capable of precisely modeling inter-chain interactions and designing protein complexes with binding capabilities from scratch. It also performs folding and inverse-folding tasks for multi-chain proteins. Moreover, APM demonstrates versatility in downstream applications: it achieves enhanced performance through supervised fine-tuning (SFT) while also supporting zero-shot sampling in certain tasks, achieving state-of-the-art results. We released our code at https: //github. com/bytedance/apm.

ICML Conference 2025 Conference Paper

Beyond Bradley-Terry Models: A General Preference Model for Language Model Alignment

• Yifan Zhang
• Ge Zhang
• Yue Wu
• Kangping Xu
• Quanquan Gu

Modeling human preferences is crucial for aligning foundation models with human values. Traditional reward modeling methods, such as the Bradley-Terry (BT) reward model, fall short in expressiveness, particularly in addressing intransitive preferences. In this paper, we introduce preference embedding, an approach that embeds responses into a latent space to capture intricate preference structures efficiently, achieving linear query complexity. Additionally, we propose preference score-based General Preference Optimization (GPO), which generalizes reward-based reinforcement learning from human feedback (RLHF). Experimental results show that our General Preference embedding Model (GPM) consistently outperforms the BT reward model on the RewardBench benchmark and effectively models cyclic preferences where any BT reward model behaves like a random guess. Furthermore, evaluations on downstream tasks such as AlpacaEval2. 0, following the language model post-training with GPO and our general preference model, reveal performance improvements over BT models. These findings indicate that our method may enhance the alignment of foundation models with nuanced human values. The code is available at https: //github. com/general-preference/general-preference-model.

ICLR Conference 2025 Conference Paper

Beyond-Expert Performance with Limited Demonstrations: Efficient Imitation Learning with Double Exploration

• Heyang Zhao
• Xingrui Yu
• David Mark Bossens
• Ivor W. Tsang
• Quanquan Gu

Imitation learning is a central problem in reinforcement learning where the goal is to learn a policy that mimics the expert's behavior. In practice, it is often challenging to learn the expert policy from a limited number of demonstrations accurately due to the complexity of the state space. Moreover, it is essential to explore the environment and collect data to achieve beyond-expert performance. To overcome these challenges, we propose a novel imitation learning algorithm called Imitation Learning with Double Exploration (ILDE), which implements exploration in two aspects: (1) optimistic policy optimization via an exploration bonus that rewards state-action pairs with high uncertainty to potentially improve the convergence to the expert policy, and (2) curiosity-driven exploration of the states that deviate from the demonstration trajectories to potentially yield beyond-expert performance. Empirically, we demonstrate that ILDE outperforms the state-of-the-art imitation learning algorithms in terms of sample efficiency and achieves beyond-expert performance on Atari and MuJoCo tasks with fewer demonstrations than in previous work. We also provide a theoretical justification of ILDE as an uncertainty-regularized policy optimization method with optimistic exploration, leading to a regret growing sublinearly in the number of episodes.

ICLR Conference 2025 Conference Paper

Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis

• Zikun Zhang
• Zixiang Chen
• Quanquan Gu

Diffusion models have achieved great success in generating high-dimensional samples across various applications. While the theoretical guarantees for continuous-state diffusion models have been extensively studied, the convergence analysis of the discrete-state counterparts remains under-explored. In this paper, we study the theoretical aspects of score-based discrete diffusion models under the Continuous Time Markov Chain (CTMC) framework. We introduce a discrete-time sampling algorithm in the general state space $[S]^d$ that utilizes score estimators at predefined time points. We derive convergence bounds for the Kullback-Leibler (KL) divergence and total variation (TV) distance between the generated sample distribution and the data distribution, considering both scenarios with and without early stopping under reasonable assumptions. Notably, our KL divergence bounds are nearly linear in the dimension $d$, aligning with state-of-the-art results for diffusion models. Our convergence analysis employs a Girsanov-based method and establishes key properties of the discrete score function, which are essential for characterizing the discrete-time sampling process.

ICLR Conference 2025 Conference Paper

CryoFM: A Flow-based Foundation Model for Cryo-EM Densities

• Yi Zhou
• Yilai Li
• Jing Yuan
• Quanquan Gu

Cryo-electron microscopy (cryo-EM) is a powerful technique in structural biology and drug discovery, enabling the study of biomolecules at high resolution. Significant advancements by structural biologists using cryo-EM have led to the production of around 40k protein density maps at various resolutions. However, cryo-EM data processing algorithms have yet to fully benefit from our knowledge of biomolecular density maps, with only a few recent models being data-driven but limited to specific tasks. In this study, we present CryoFM, a foundation model designed as a generative model, learning the distribution of high-quality density maps and generalizing effectively to downstream tasks. Built on flow matching, CryoFM is trained to accurately capture the prior distribution of biomolecular density maps. Furthermore, we introduce a flow posterior sampling method that leverages CryoFM as a flexible prior for several downstream tasks in cryo-EM and cryo-electron tomography (cryo-ET) without the need for fine-tuning, achieving state-of-the-art performance on most tasks and demonstrating its potential as a foundational model for broader applications in these fields.

TMLR Journal 2025 Journal Article

Decomposed Direct Preference Optimization for Structure-Based Drug Design

• Xiwei Cheng
• Xiangxin Zhou
• Yuwei Yang
• Yu Bao
• Quanquan Gu

Diffusion models have achieved promising results for Structure-Based Drug Design (SBDD). Nevertheless, high-quality protein subpocket and ligand data are relatively scarce, which hinders the models’ generation capabilities. Recently, Direct Preference Optimization (DPO) has emerged as a pivotal tool for aligning generative models with human preferences. In this paper, we propose DecompDpo, a structure-based optimization method aligns diffusion models with pharmaceutical needs using multi-granularity preference pairs. DecompDpo introduces decomposition into the optimization objectives and obtains preference pairs at the molecule or decomposed substructure level based on each objective’s decomposability. Additionally, DecompDpo introduces a physics-informed energy term to ensure reasonable molecular conformations in the optimization results. Notably, DecompDpo can be effectively used for two main purposes: (1) fine-tuning pretrained diffusion models for molecule generation across various protein families, and (2) molecular optimization given a specific protein subpocket after generation. Extensive experiments on the CrossDocked2020 benchmark show that DecompDpo significantly improves model performance, achieving up to 98.5% Med. High Affinity and a 43.9% success rate for molecule generation, and 100% Med. High Affinity and a 52.1% success rate for targeted molecule optimization.

ICML Conference 2025 Conference Paper

Designing Cyclic Peptides via Harmonic SDE with Atom-Bond Modeling

• Xiangxin Zhou
• Mingyu Li
• Yi Xiao
• Jiahan Li
• Dongyu Xue
• Zaixiang Zheng
• Jianzhu Ma
• Quanquan Gu

Cyclic peptides offer inherent advantages in pharmaceuticals. For example, cyclic peptides are more resistant to enzymatic hydrolysis compared to linear peptides and usually exhibit excellent stability and affinity. Although deep generative models have achieved great success in linear peptide design, several challenges prevent the development of computational methods for designing diverse types of cyclic peptides. These challenges include the scarcity of 3D structural data on target proteins and associated cyclic peptide ligands, the geometric constraints that cyclization imposes, and the involvement of non-canonical amino acids in cyclization. To address the above challenges, we introduce CpSDE, which consists of two key components: AtomSDE, a generative structure prediction model based on harmonic SDE, and ResRouter, a residue type predictor. Utilizing a routed sampling algorithm that alternates between these two models to iteratively update sequences and structures, CpSDE facilitates the generation of cyclic peptides. By employing explicit all-atom and bond modeling, CpSDE overcomes existing data limitations and is proficient in designing a wide variety of cyclic peptides. Our experimental results demonstrate that the cyclic peptides designed by our method exhibit reliable stability and affinity.

ICLR Conference 2025 Conference Paper

DPLM-2: A Multimodal Diffusion Protein Language Model

• Xinyou Wang
• Zaixiang Zheng
• Fei Ye
• Dongyu Xue
• Shujian Huang
• Quanquan Gu

Proteins are essential macromolecules defined by their amino acid sequences, which determine their three-dimensional structures and, consequently, their functions in all living organisms. Therefore, generative protein modeling necessitates a multimodal approach to simultaneously model, understand, and generate both sequences and structures. However, existing methods typically use separate models for each modality, limiting their ability to capture the intricate relationships between sequence and structure. This results in suboptimal performance in tasks that requires joint understanding and generation of both modalities. In this paper, we introduce DPLM-2, a multimodal protein foundation model that extends discrete diffusion protein language model (DPLM) to accommodate both sequences and structures. To enable structural learning with the language model, 3D coordinates are converted to discrete tokens using a lookup-free quantization-based tokenizer. By training on both experimental and high-quality synthetic structures, DPLM-2 learns the joint distribution of sequence and structure, as well as their marginals and conditionals. We also implement an efficient warm-up strategy to exploit the connection between large-scale evolutionary data and structural inductive biases from pre-trained sequence-based protein language models. Empirical evaluation shows that DPLM-2 can simultaneously generate highly compatible amino acid sequences and their corresponding 3D structures eliminating the need for a two-stage generation approach. Moreover, DPLM-2 demonstrates competitive performance in various conditional generation tasks, including folding, inverse folding, and scaffolding with multimodal motif inputs.

ICML Conference 2025 Conference Paper

Elucidating the Design Space of Multimodal Protein Language Models

• Cheng-Yen Hsieh
• Xinyou Wang
• Daiheng Zhang
• Dongyu Xue
• Fei Ye
• Shujian Huang
• Zaixiang Zheng
• Quanquan Gu

Multimodal protein language models (PLMs) integrate sequence and token-based structural information, serving as a powerful foundation for protein modeling, generation, and design. However, the reliance on tokenizing 3D structures into discrete tokens causes substantial loss of fidelity about fine-grained structural details and correlations. In this paper, we systematically elucidate the design space of multimodal PLMs to overcome their limitations. We identify tokenization loss and inaccurate structure token predictions by the PLMs as major bottlenecks. To address these, our proposed design space covers improved generative modeling, structure-aware architectures and representation learning, and data exploration. Our advancements approach finer-grained supervision, demonstrating that token-based multimodal PLMs can achieve robust structural modeling. The effective design methods dramatically improve the structure generation diversity, and notably, folding abilities of our 650M model by reducing the RMSD from 5. 52 to 2. 36 on PDB testset, even outperforming 3B baselines and on par with the specialized folding models. Project page and code: https: //bytedance. github. io/dplm/dplm-2. 1.

ICLR Conference 2025 Conference Paper

Energy-Weighted Flow Matching for Offline Reinforcement Learning

• Shiyuan Zhang
• Weitong Zhang
• Quanquan Gu

This paper investigates energy guidance in generative modeling, where the target distribution is defined as $q(\mathbf x) \propto p(\mathbf x)\exp(-\beta \mathcal E(\mathbf x))$, with $p(\mathbf x)$ being the data distribution and $\mathcal E(\mathbf x)$ as the energy function. To comply with energy guidance, existing methods often require auxiliary procedures to learn intermediate guidance during the diffusion process. To overcome this limitation, we explore energy-guided flow matching, a generalized form of the diffusion process. We introduce energy-weighted flow matching (EFM), a method that directly learns the energy-guided flow without the need for auxiliary models. Theoretical analysis shows that energy-weighted flow matching accurately captures the guided flow. Additionally, we extend this methodology to energy-weighted diffusion models and apply it to offline reinforcement learning (RL) by proposing the Q-weighted Iterative Policy Optimization (QIPO). Empirically, we demonstrate that the proposed QIPO algorithm improves performance in offline RL tasks. Notably, our algorithm is the first energy-guided diffusion model that operates independently of auxiliary models and the first exact energy-guided flow matching model in the literature.

ICML Conference 2025 Conference Paper

Global Convergence and Rich Feature Learning in L-Layer Infinite-Width Neural Networks under μ Parametrization

• Zixiang Chen
• Greg Yang
• Qingyue Zhao 0001
• Quanquan Gu

Despite deep neural networks’ powerful representation learning capabilities, theoretical understanding of how networks can simultaneously achieve meaningful feature learning and global convergence remains elusive. Existing approaches like the neural tangent kernel (NTK) are limited because features stay close to their initialization in this parametrization, leaving open questions about feature properties during substantial evolution. In this paper, we investigate the training dynamics of infinitely wide, $L$-layer neural networks using the tensor program (TP) framework. Specifically, we show that, when trained with stochastic gradient descent (SGD) under the Maximal Update parametrization ($\mu$P) and mild conditions on the activation function, SGD enables these networks to learn linearly independent features that substantially deviate from their initial values. This rich feature space captures relevant data information and ensures that any convergent point of the training process is a global minimum. Our analysis leverages both the interactions among features across layers and the properties of Gaussian random variables, providing new insights into deep representation learning. We further validate our theoretical findings through experiments on real-world datasets.

TMLR Journal 2025 Journal Article

Guided Discrete Diffusion for Electronic Health Record Generation

• Jun Han
• Zixiang Chen
• Yongqian Li
• Yiwen Kou
• Eran Halperin
• Robert E. Tillman
• Quanquan Gu

Electronic health records (EHRs) are a pivotal data source that enables numerous applications in computational medicine, e.g., disease progression prediction, clinical trial design, and health economics and outcomes research. Despite wide usability, their sensitive nature raises privacy and confidentially concerns, which limit potential use cases. To tackle these challenges, we explore the use of generative models to synthesize artificial, yet realistic EHRs. While diffusion-based methods have recently demonstrated state-of-the-art performance in generating other data modalities and overcome the training instability and mode collapse issues that plague previous GAN-based approaches, their applications in EHR generation remain underexplored. The discrete nature of tabular medical code data in EHRs poses challenges for high-quality data generation, especially for continuous diffusion models. To this end, we introduce a novel tabular EHR generation method, EHR-D3PM, which enables both unconditional and conditional generation using the discrete diffusion model. Our experiments demonstrate that EHR-D3PM significantly outperforms existing generative baselines on comprehensive fidelity and utility metrics while maintaining less attribute and membership vulnerability risks. Furthermore, we show EHR-D3PM is effective as a data augmentation method and enhances performance on downstream tasks when combined with real data.

ICML Conference 2025 Conference Paper

Logarithmic Regret for Online KL-Regularized Reinforcement Learning

• Heyang Zhao
• Chenlu Ye
• Wei Xiong 0015
• Quanquan Gu
• Tong Zhang 0001

Recent advances in Reinforcement Learning from Human Feedback (RLHF) have shown that KL-regularization plays a pivotal role in improving the efficiency of RL fine-tuning for large language models (LLMs). Despite its empirical advantage, the theoretical difference between KL-regularized RL and standard RL remains largely under-explored. While there is a recent line of work on the theoretical analysis of KL-regularized objective in decision making (Xiong et al. , 2024a; Xie et al. , 2024; Zhao et al. , 2024), these analyses either reduce to the traditional RL setting or rely on strong coverage assumptions. In this paper, we propose an optimism-based KL-regularized online contextual bandit algorithm, and provide a novel analysis of its regret. By carefully leveraging the benign optimization landscape induced by the KL-regularization and the optimistic reward estimation, our algorithm achieves an $\mathcal{O}\big(\eta\log (N_{\mathcal R} T)\cdot d_{\mathcal R}\big)$ logarithmic regret bound, where $\eta, N_{\mathcal R}, T, d_{\mathcal R}$ denote the KL-regularization parameter, the cardinality of the reward function class, number of rounds, and the complexity of the reward function class. Furthermore, we extend our algorithm and analysis to reinforcement learning by developing a novel decomposition over transition steps and also obtain a similar logarithmic regret bound.

ICML Conference 2025 Conference Paper

MARS: Unleashing the Power of Variance Reduction for Training Large Models

• Huizhuo Yuan
• Yifeng Liu 0004
• Shuang Wu
• Xun Zhou
• Quanquan Gu

Training deep neural networks–and more recently, large models–demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS ( M ake v A riance R eduction S hine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.

ICML Conference 2025 Conference Paper

Mitigating Object Hallucination in Large Vision-Language Models via Image-Grounded Guidance

• Linxi Zhao
• Yihe Deng
• Weitong Zhang
• Quanquan Gu

The advancement of Large Vision-Language Models (LVLMs) has increasingly highlighted the critical issue of their tendency to hallucinate non-existing objects in the images. To address this issue, previous works focused on using specially curated datasets or powerful LLMs to rectify the outputs of LVLMs. However, these approaches require either costly training or fine-tuning, or API access to proprietary LLMs for post-generation correction. In response to these limitations, we propose Mitigating hallucinAtion via image-gRounded guIdaNcE (MARINE), a framework that is both training-free and API-free. MARINE effectively and efficiently reduces object hallucinations during inference by introducing image-grounded guidance to LVLMs. This is achieved by leveraging open-source vision models to extract object-level information, thereby enhancing the precision of LVLM-generated content. Our framework’s flexibility further allows for the integration of multiple vision models, enabling more reliable and robust object-level guidance. Through comprehensive evaluations across 5 popular LVLMs with diverse evaluation metrics and benchmarks, we demonstrate the effectiveness of MARINE, which even outperforms existing fine-tuning-based methods. Remarkably, it reduces hallucinations consistently in GPT-4V-assisted evaluation while maintaining the detailedness of LVLMs’ generations. We release our code at https: //github. com/Linxi-ZHAO/MARINE.

ICML Conference 2025 Conference Paper

Nearly Optimal Algorithms for Contextual Dueling Bandits from Adversarial Feedback

• Qiwei Di
• Jiafan He
• Quanquan Gu

Learning from human feedback plays an important role in aligning generative models, such as large language models (LLM). However, the effectiveness of this approach can be influenced by adversaries, who may intentionally provide misleading preferences to manipulate the output in an undesirable or harmful direction. To tackle this challenge, we study a specific model within this problem domain–contextual dueling bandits with adversarial feedback, where the true preference label can be flipped by an adversary. We propose an algorithm namely robust contextual dueling bandits ($\texttt{RCDB}$), which is based on uncertainty-weighted maximum likelihood estimation. Our algorithm achieves an $\tilde O(d\sqrt{T}/\kappa+dC/\kappa)$ regret bound, where $T$ is the number of rounds, $d$ is the dimension of the context, $\kappa$ is the lower bound of the derivative of the link function, and $ 0 \le C \le T$ is the total number of adversarial feedback. We also prove a lower bound to show that our regret bound is nearly optimal, both in scenarios with and without ($C=0$) adversarial feedback. Our work is the first to achieve nearly minimax optimal regret for dueling bandits in the presence of adversarial preference feedback. Additionally, for the sigmoid link function, we develop a novel algorithm that takes into account the effect of local derivatives into maximum likelihood estimation (MLE) analysis through a refined method for estimating the link function’s derivative. This method helps us to eliminate the $\kappa$ dependence in the leading term with respect to $T$, which reduces the exponential dependence on the parameter radius $B$ to a polynomial dependence. We conduct experiments to evaluate our proposed algorithm $\texttt{RCDB}$ against various types of adversarial feedback. Experimental results demonstrate its superiority over the state-of-the-art dueling bandit algorithms in the presence of adversarial feedback.

ICLR Conference 2025 Conference Paper

ProteinBench: A Holistic Evaluation of Protein Foundation Models

• Fei Ye
• Zaixiang Zheng
• Dongyu Xue
• Yuning Shen
• Lihao Wang
• Yiming Ma
• Yan Wang
• Xinyou Wang

Recent years have witnessed a surge in the development of protein foundation models, significantly improving performance in protein prediction and generative tasks ranging from 3D structure prediction and protein design to conformational dynamics. However, the capabilities and limitations associated with these models remain poorly understood due to the absence of a unified evaluation framework. To fill this gap, we introduce ProteinBench, a holistic evaluation framework designed to enhance the transparency of protein foundation models. Our approach consists of three key components: (i) A taxonomic classification of tasks that broadly encompass the main challenges in the protein domain, based on the relationships between different protein modalities; (ii) A multi-metric evaluation approach that assesses performance across four key dimensions: quality, novelty, diversity, and robustness; and (iii) In-depth analyses from various user objectives, providing a holistic view of model performance. Our comprehensive evaluation of protein foundation models reveals several key findings that shed light on their current capabilities and limitations. To promote transparency and facilitate further research, we release the evaluation dataset, code, and a public leaderboard publicly for further analysis and a general modular toolkit. We intend for ProteinBench to be a living benchmark for establishing a standardized, in-depth evaluation framework for protein foundation models, driving their development and application while fostering collaboration within the field.

ICML Conference 2025 Conference Paper

Ranking with Multiple Oracles: From Weak to Strong Stochastic Transitivity

• Tao Jin 0002
• Yue Wu
• Quanquan Gu
• Farzad Farnoud

We study the problem of efficiently aggregating the preferences of items from multiple information sources (oracles) and infer the ranking under both the weak stochastic transitivity (WST) and the strong stochastic transitivity (SST) conditions. When the underlying preference model satisfies the WST condition, we propose an algorithm named RMO-WST, which has a bi-level design: at the higher level, it actively allocates comparison budgets to all undetermined pairs until the full ranking is recovered; at the lower level, it attempts to compare the pair of items and selects the more accurate oracles simultaneously. We prove that the sample complexity of RMO-WST is $ \tilde O( N\sum_{i=2}^{N}H_{\sigma^{-1}(i), {\sigma^{-1}(i-1)}} )$, where $N$ is the number of items to rank, $H$ is a problem-dependent hardness factor, and $\sigma^{-1}(i)$ represents the $i$-th best item. We also provide a tight lower bound that matches the upper bound of approximate ranking under the WST condition, answering a previously open problem. In addition, when the SST condition is satisfied, we propose an algorithm named RMO-SST, which can achieve an $\tilde{O}(\sum_{i=1}^{N} H_i \log(N))$ sample complexity. This outperforms the best-known sample complexity by a factor of $\log(N)$. The theoretical advantages of our algorithms are verified by empirical experiments in a simulated environment.

TMLR Journal 2025 Journal Article

Reinforcement Learning from Human Feedback with Active Queries

• Kaixuan Ji
• Jiafan He
• Quanquan Gu

Aligning large language models (LLM) with human preference plays a key role in building modern generative models and can be achieved by reinforcement learning from human feedback (RLHF). Despite their superior performance, current RLHF approaches often require a large amount of human-labelled preference data, which is expensive to collect. In this paper, inspired by the success of active learning, we address this problem by proposing query-efficient RLHF methods. We first formalize the alignment problem as a contextual dueling bandit problem and design an active-query-based proximal policy optimization (APPO) algorithm with an $\tilde{O}(d^2/\Delta)$ instance-dependent regret bound and an $\tilde{O}(d^2/\Delta^2)$ query complexity, where $d$ is the dimension of feature space and $\Delta$ is the sub-optimality gap over all the contexts. We then propose ADPO, a practical version of our algorithm based on direct preference optimization (DPO) and apply it to fine-tuning LLMs. Our experiments show that ADPO, while only making about half of queries for human preference, matches the performance of DPO, establishing it as a data-efficient alternative to DPO. The codes are available at https://github.com/jkx19/ActiveQuery.

ICLR Conference 2025 Conference Paper

Self-Play Preference Optimization for Language Model Alignment

• Yue Wu
• Zhiqing Sun
• Huizhuo Yuan
• Kaixuan Ji
• Yiming Yang 0002
• Quanquan Gu

Standard reinforcement learning from human feedback (RLHF) approaches relying on parametric models like the Bradley-Terry model fall short in capturing the intransitivity and irrationality in human preferences. Recent advancements suggest that directly working with preference probabilities can yield a more accurate reflection of human preferences, enabling more flexible and accurate language model alignment. In this paper, we propose a self-play-based method for language model alignment, which treats the problem as a constant-sum two-player game aimed at identifying the Nash equilibrium policy. Our approach, dubbed *Self-Play Preference Optimization* (SPPO), utilizes iterative policy updates to provably approximate the Nash equilibrium. Additionally, we propose a new SPPO objective which is both strongly motivated by theory and is simple and effective in practice. In our experiments, using only 60k prompts (without responses) from the UltraFeedback dataset and without any prompt augmentation, by leveraging a pre-trained preference model PairRM with only 0.4B parameters, SPPO can obtain a model from fine-tuning Mistral-7B-Instruct-v0.2 that achieves the state-of-the-art length-controlled win-rate of 28.53\% against GPT-4-Turbo on AlpacaEval 2.0. It also outperforms the (iterative) DPO and IPO on MT-Bench, Arena-Hard, and the Open LLM Leaderboard. Starting from a stronger base model Llama-3-8B-Instruct, we are able to achieve a length-controlled win rate of 38.77\%. Notably, the strong performance of SPPO is achieved without additional external supervision (e.g., responses, preferences, etc.) from GPT-4 or other stronger language models.

NeurIPS Conference 2025 Conference Paper

Sharp Analysis for KL-Regularized Contextual Bandits and RLHF

• Heyang Zhao
• Chenlu Ye
• Quanquan Gu
• Tong Zhang

Reverse-Kullback-Leibler (KL) regularization has emerged to be a predominant technique to enhance policy optimization in reinforcement learning (RL) and reinforcement learning from human feedback (RLHF), which forces the learned policy to stay close to a reference policy. While the effectiveness of KL-regularization has been empirically demonstrated in various practical scenarios, current theoretical analyses of KL-regularized RLHF still yield the same $\mathcal{O}(1 / \epsilon^2)$ sample complexity as ones without KL-regularization. To understand the fundamental distinction between objectives with KL-regularization and ones without KL-regularization, we are the first to theoretically demonstrate the power of KL-regularization by providing a sharp analysis for KL-regularized contextual bandits and RLHF, revealing an $\mathcal{O}(1 / \epsilon)$ sample complexity when $\epsilon$ is sufficiently small. We also prove matching lower bounds for both settings. More specifically, we study how the coverage of the reference policy affects the sample complexity of KL-regularized online contextual bandits and RLHF. We show that with sufficient coverage from the reference policy, a simple two-stage mixed sampling algorithm can achieve an $\mathcal{O}(1 / \epsilon)$ sample complexity with only an additive dependence on the coverage coefficient, thus proving the benefits of online data even without explicit exploration. Our results provide a comprehensive understanding of the roles of KL-regularization and data coverage in online decision making, shedding light on the design of more efficient algorithms.

NeurIPS Conference 2025 Conference Paper

Simultaneous Modeling of Protein Conformation and Dynamics via Autoregression

• Yuning Shen
• Lihao Wang
• Huizhuo Yuan
• Yan Wang
• Bangji Yang
• Quanquan Gu

Understanding protein dynamics is critical for elucidating their biological functions. The increasing availability of molecular dynamics (MD) data enables the training of deep generative models to efficiently explore the conformational space of proteins. However, existing approaches either fail to explicitly capture the temporal dependencies between conformations or do not support direct generation of time-independent samples. To address these limitations, we introduce ConfRover, an autoregressive model that simultaneously learns protein conformation and dynamics from MD trajectory data, supporting both time-dependent and time-independent sampling. At the core of our model is a modular architecture comprising: (i) an encoding layer, adapted from protein folding models, that embeds protein-specific information and conformation at each time frame into a latent space; (ii) a temporal module, a sequence model that captures conformational dynamics across frames; and (iii) an SE(3) diffusion model as the structure decoder, generating conformations in continuous space. Experiments on ATLAS, a large-scale protein MD dataset of diverse structures, demonstrate the effectiveness of our model in learning conformational dynamics and supporting a wide range of downstream tasks. ConfRover is the first model to sample both protein conformations and trajectories within a single framework, offering a novel and flexible approach for learning from protein MD data.

NeurIPS Conference 2025 Conference Paper

Tensor Product Attention Is All You Need

• Yifan Zhang
• Yifeng Liu
• Huizhuo Yuan
• Zhen Qin
• Yang Yuan
• Quanquan Gu
• Andrew Yao

Scaling language models to handle longer input sequences typically necessitates large key-value (KV) caches, resulting in substantial memory overhead during inference. In this paper, we propose Tensor Product Attention (TPA), a novel attention mechanism that uses tensor decompositions to represent queries, keys, and values compactly, substantially shrinking the KV cache size at inference time. By factorizing these representations into contextual low-rank components and seamlessly integrating with Rotary Position Embedding (RoPE), TPA achieves improved model quality alongside memory efficiency. Based on TPA, we introduce the Tensor ProducT ATTenTion Transformer (T6), a new model architecture for sequence modeling. Through extensive empirical evaluation on language modeling tasks, we demonstrate that T6 surpasses or matches the performance of standard Transformer baselines including Multi-Head Attention (MHA), Multi-Query Attention (MQA), Grouped-Query Attention (GQA), and Multi-Head Latent Attention (MLA) across various metrics, including perplexity and a range of established evaluation benchmarks. Notably, TPA's memory efficiency and computational efficiency at decoding stage enables processing longer sequences under fixed resource constraints, addressing a critical scalability challenge in modern language models. Project Page: https: //github. com/tensorgi/TPA.

ICLR Conference 2025 Conference Paper

Unified Convergence Analysis for Score-Based Diffusion Models with Deterministic Samplers

• Runjia Li
• Qiwei Di
• Quanquan Gu

Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a known prior distribution, and second, sampling to recover the original data distribution from noise. Among the various sampling methods, deterministic samplers stand out for their enhanced efficiency. However, analyzing these deterministic samplers presents unique challenges, as they preclude the use of established techniques such as Girsanov's theorem, which are only applicable to stochastic samplers. Furthermore, existing analysis for deterministic samplers usually focuses on specific examples, lacking a generalized approach for general forward processes and various deterministic samplers. Our paper addresses these limitations by introducing a unified convergence analysis framework. To demonstrate the power of our framework, we analyze the variance-preserving (VP) forward process with the exponential integrator (EI) scheme, achieving iteration complexity of $\tilde{O}(d^2/\epsilon)$. Additionally, we provide a detailed analysis of Denoising Diffusion Implicit Models (DDIM)-type samplers, which have been underexplored in previous research, achieving polynomial iteration complexity.

NeurIPS Conference 2025 Conference Paper

Variance-Aware Feel-Good Thompson Sampling for Contextual Bandits

• Xuheng Li
• Quanquan Gu

Variance-dependent regret bounds have received increasing attention in recent studies on contextual bandits. However, most of these studies are focused on upper confidence bound (UCB)-based bandit algorithms, while sampling based bandit algorithms such as Thompson sampling are still understudied. The only exception is the `LinVDTS` algorithm (Xu et al. , 2023), which is limited to linear reward function and its regret bound is not optimal with respect to the model dimension. In this paper, we present `FGTSVA`, a variance-aware Thompson Sampling algorithm for contextual bandits with general reward function with optimal regret bound. At the core of our analysis is an extension of the decoupling coefficient, a technique commonly used in the analysis of Feel-good Thompson sampling (FGTS) that reflects the complexity of the model space. With the new decoupling coefficient denoted by $\mathrm{dc}$, `FGTS-VA` achieves the regret of $\tilde{\mathcal{O}}(\sqrt{\mathrm{dc}\cdot\log|\mathcal{F}|\sum_{t=1}^T\sigma_t^2}+\mathrm{dc})$, where $|\mathcal{F}|$ is the size of the model space, $T$ is the total number of rounds, and $\sigma_t^2$ is the subgaussian norm of the noise (e. g. , variance when the noise is Gaussian) at round $t$. In the setting of contextual linear bandits, the regret bound of `FGTSVA` matches that of UCB-based algorithms using weighted linear regression (Zhou and Gu, 2022).

NeurIPS Conference 2024 Conference Paper

A Nearly Optimal and Low-Switching Algorithm for Reinforcement Learning with General Function Approximation

• Heyang Zhao
• Jiafan He
• Quanquan Gu

The exploration-exploitation dilemma has been a central challenge in reinforcement learning (RL) with complex model classes. In this paper, we propose a new algorithm, Monotonic Q-Learning with Upper Confidence Bound (MQL-UCB) for RL with general function approximation. Our key algorithmic design includes (1) a general deterministic policy-switching strategy that achieves low switching cost, (2) a monotonic value function structure with carefully controlled function class complexity, and (3) a variance-weighted regression scheme that exploits historical trajectories with high data efficiency. MQL-UCB achieves minimax optimal regret of $\tilde{O}(d\sqrt{HK})$ when $K$ is sufficiently large and near-optimal policy switching cost of $\tilde{O}(dH)$, with $d$ being the eluder dimension of the function class, $H$ being the planning horizon, and $K$ being the number of episodes. Our work sheds light on designing provably sample-efficient and deployment-efficient Q-learning with nonlinear function approximation.

NeurIPS Conference 2024 Conference Paper

Achieving Constant Regret in Linear Markov Decision Processes

• Weitong Zhang
• Zhiyuan Fan
• Jiafan He
• Quanquan Gu

We study the constant regret guarantees in reinforcement learning (RL). Our objective is to design an algorithm that incurs only finite regret over infinite episodes with high probability. We introduce an algorithm, Cert-LSVI-UCB, for misspecified linear Markov decision processes (MDPs) where both the transition kernel and the reward function can be approximated by some linear function up to misspecification level $\zeta$. At the core of Cert-LSVI-UCB is an innovative certified estimator, which facilitates a fine-grained concentration analysis for multi-phase value-targeted regression, enabling us to establish an instance-dependent regret bound that is constant w. r. t. the number of episodes. Specifically, we demonstrate that for a linear MDP characterized by a minimal suboptimality gap $\Delta$, Cert-LSVI-UCB has a cumulative regret of $\tilde{\mathcal{O}}(d^3H^5/\Delta)$ with high probability, provided that the misspecification level $\zeta$ is below $\tilde{\mathcal{O}}(\Delta / (\sqrt{d}H^2))$. Here $d$ is the dimension of the feature space and $H$ is the horizon. Remarkably, this regret bound is independent of the number of episodes $K$. To the best of our knowledge, Cert-LSVI-UCB is the first algorithm to achieve a constant, instance-dependent, high-probability regret bound in RL with linear function approximation without relying on prior distribution assumptions.

NeurIPS Conference 2024 Conference Paper

Antigen-Specific Antibody Design via Direct Energy-based Preference Optimization

• Xiangxin Zhou
• Dongyu Xue
• Ruizhe Chen
• Zaixiang Zheng
• Liang Wang
• Quanquan Gu

Antibody design, a crucial task with significant implications across various disciplines such as therapeutics and biology, presents considerable challenges due to its intricate nature. In this paper, we tackle antigen-specific antibody sequence-structure co-design as an optimization problem towards specific preferences, considering both rationality and functionality. Leveraging a pre-trained conditional diffusion model that jointly models sequences and structures of antibodies with equivariant neural networks, we propose direct energy-based preference optimization to guide the generation of antibodies with both rational structures and considerable binding affinities to given antigens. Our method involves fine-tuning the pre-trained diffusion model using a residue-level decomposed energy preference. Additionally, we employ gradient surgery to address conflicts between various types of energy, such as attraction and repulsion. Experiments on RAbD benchmark show that our approach effectively optimizes the energy of generated antibodies and achieves state-of-the-art performance in designing high-quality antibodies with low total energy and high binding affinity simultaneously, demonstrating the superiority of our approach.

ICML Conference 2024 Conference Paper

Borda Regret Minimization for Generalized Linear Dueling Bandits

• Yue Wu
• Tao Jin 0002
• Qiwei Di
• Hao Lou
• Farzad Farnoud
• Quanquan Gu

Dueling bandits are widely used to model preferential feedback prevalent in many applications such as recommendation systems and ranking. In this paper, we study the Borda regret minimization problem for dueling bandits, which aims to identify the item with the highest Borda score while minimizing the cumulative regret. We propose a rich class of generalized linear dueling bandit models, which cover many existing models. We first prove a regret lower bound of order $\Omega(d^{2/3} T^{2/3})$ for the Borda regret minimization problem, where $d$ is the dimension of contextual vectors and $T$ is the time horizon. To attain this lower bound, we propose an explore-then-commit type algorithm for the stochastic setting, which has a nearly matching regret upper bound $\tilde{O}(d^{2/3} T^{2/3})$. We also propose an EXP3-type algorithm for the adversarial linear setting, where the underlying model parameter can change in each round. Our algorithm achieves an $\tilde{O}(d^{2/3} T^{2/3})$ regret, which is also optimal. Empirical evaluations on both synthetic data and a simulated real-world environment are conducted to corroborate our theoretical analysis.

ICLR Conference 2024 Conference Paper

DecompOpt: Controllable and Decomposed Diffusion Models for Structure-based Molecular Optimization

• Xiangxin Zhou
• Xiwei Cheng
• Yuwei Yang
• Yu Bao
• Liang Wang 0001
• Quanquan Gu

Recently, 3D generative models have shown promising performances in structure-based drug design by learning to generate ligands given target binding sites. However, only modeling the target-ligand distribution can hardly fulfill one of the main goals in drug discovery -- designing novel ligands with desired properties, e.g., high binding affinity, easily synthesizable, etc. This challenge becomes particularly pronounced when the target-ligand pairs used for training do not align with these desired properties. Moreover, most existing methods aim at solving de novo design task, while many generative scenarios requiring flexible controllability, such as R-group optimization and scaffold hopping, have received little attention. In this work, we propose DecompOpt, a structure-based molecular optimization method based on a controllable and decomposed diffusion model. DecompOpt presents a new generation paradigm which combines optimization with conditional diffusion models to achieve desired properties while adhering to the molecular grammar. Additionally, DecompOpt offers a unified framework covering both de novo design and controllable generation. To achieve so, ligands are decomposed into substructures which allows fine-grained control and local optimization. Experiments show that DecompOpt can efficiently generate molecules with improved properties than strong de novo baselines, and demonstrate great potential in controllable generation tasks.

ICML Conference 2024 Conference Paper

Diffusion Language Models Are Versatile Protein Learners

• Xinyou Wang
• Zaixiang Zheng
• Fei Ye
• Dongyu Xue
• Shujian Huang
• Quanquan Gu

This paper introduces diffusion protein language model (DPLM), a versatile protein language model that demonstrates strong generative and predictive capabilities for protein sequences. We first pre-train scalable DPLMs from evolutionary-scale protein sequences within a generative self-supervised discrete diffusion probabilistic framework, which generalizes language modeling for proteins in a principled way. After pre-training, DPLM exhibits the ability to generate structurally plausible, novel and diverse protein sequences for unconditional generation. We further demonstrate the proposed diffusion generative pre-training make DPLM possess a better understanding of proteins, making it a superior representation learner, which can be fine-tuned for various predictive tasks, comparing favorably to ESM2. Moreover, DPLM can be tailored for various needs, which showcases its prowess of conditional generation in several ways: (1) conditioning on partial peptide sequences, e. g. , generating scaffolds for functional motifs with high success rate; (2) incorporating other modalities as conditioners, e. g. , structure-conditioned generation for inverse folding; and (3) steering sequence generation towards desired properties, e. g. , satisfying specified secondary structures, through a plug-and-play classifier guidance.

NeurIPS Conference 2024 Conference Paper

Enhancing Large Vision Language Models with Self-Training on Image Comprehension

• Yihe Deng
• Pan Lu
• Fan Yin
• Ziniu Hu
• Sheng Shen
• Quanquan Gu
• James Zou
• Kai-Wei Chang

Large vision language models (LVLMs) integrate large language models (LLMs) with pre-trained vision encoders, thereby activating the perception capability of the model to understand image inputs for different queries and conduct subsequent reasoning. Improving this capability requires high-quality vision-language data, which is costly and labor-intensive to acquire. Self-training approaches have been effective in single-modal settings to alleviate the need for labeled data by leveraging model's own generation. However, effective self-training remains a challenge regarding the unique visual perception and reasoning capability of LVLMs. To address this, we introduce S elf- T raining on I mage C omprehension ( STIC ), which emphasizes a self-training approach specifically for image comprehension. First, the model self-constructs a preference dataset for image descriptions using unlabeled images. Preferred responses are generated through a step-by-step prompt, while dis-preferred responses are generated from either corrupted images or misleading prompts. To further self-improve reasoning on the extracted visual information, we let the model reuse a small portion of existing instruction-tuning data and append its self-generated image descriptions to the prompts. We validate the effectiveness of STIC across seven different benchmarks, demonstrating substantial performance gains of 4. 0% on average while using 70% less supervised fine-tuning data than the current method. Further studies dive into various components of STIC and highlight its potential to leverage vast quantities of unlabeled images for self-training.

NeurIPS Conference 2024 Conference Paper

Fast Sampling via Discrete Non-Markov Diffusion Models with Predetermined Transition Time

• Zixiang Chen
• Huizhuo Yuan
• Yongqian Li
• Yiwen Kou
• Junkai Zhang
• Quanquan Gu

Discrete diffusion models have emerged as powerful tools for high-quality data generation. Despite their success in discrete spaces, such as text generation tasks, the acceleration of discrete diffusion models remains under-explored. In this paper, we propose discrete non-Markov diffusion models (DNDM), which naturally induce the predetermined transition time set. This enables a training-free sampling algorithm that significantly reduces the number of function evaluations (i. e. , calls to the neural network), making the sampling process much faster. Furthermore, we study the transition from finite to infinite step sampling, offering new insights into bridging the gap between discrete and continuous-time processes for discrete diffusion models. Extensive experiments on natural language generation and machine translation tasks demonstrate the superior performance of our method in terms of both generation speed and sample quality compared to existing methods for discrete diffusion models. Codes are available at \url{https: //github. com/uclaml/DNDM}.

ICML Conference 2024 Conference Paper

Feel-Good Thompson Sampling for Contextual Dueling Bandits

• Xuheng Li
• Heyang Zhao
• Quanquan Gu

Contextual dueling bandits, where a learner compares two options based on context and receives feedback indicating which was preferred, extends classic dueling bandits by incorporating contextual information for decision-making and preference learning. Several algorithms based on the upper confidence bound (UCB) have been proposed for linear contextual dueling bandits. However, no algorithm based on posterior sampling has been developed in this setting, despite the empirical success observed in traditional contextual bandits. In this paper, we propose a Thompson sampling algorithm, named FGTS. CDB, for linear contextual dueling bandits. At the core of our algorithm is a new Feel-Good exploration term specifically tailored for dueling bandits. This term leverages the independence of the two selected arms, thereby avoiding a cross term in the analysis. We show that our algorithm achieves nearly minimax-optimal regret, i. e. , $\tilde{\mathcal{O}}(d\sqrt T)$, where $d$ is the model dimension and $T$ is the time horizon. Finally, we evaluate our algorithm on synthetic data and observe that FGTS. CDB outperforms existing algorithms by a large margin.

ICLR Conference 2024 Conference Paper

Horizon-free Reinforcement Learning in Adversarial Linear Mixture MDPs

• Kaixuan Ji
• Qingyue Zhao 0001
• Jiafan He
• Weitong Zhang
• Quanquan Gu

Recent studies have shown that the regret of reinforcement learning (RL) can be polylogarithmic in the planning horizon $H$. However, it remains an open question whether such a result holds for adversarial RL. In this paper, we answer this question affirmatively by proposing the first horizon-free policy search algorithm. To tackle the challenges caused by exploration and adversarially chosen reward over episodes, our algorithm employs (1) a variance-uncertainty-aware weighted least square estimator for the transition kernel; and (2) an occupancy measure-based technique for the online search of a stochastic policy. We show that our algorithm achieves an $\tilde{O}\big((d+\log |\mathcal{S}|)\sqrt{K} + d^2\big)$ regret with full-information feedback, where $d$ is the dimension of a known feature mapping linearly parametrizing the unknown transition kernel of the MDP, $K$ is the number of episodes, $|\mathcal{S}|$ is the cardinality of the state space. We also provide hardness results to justify the near optimality of our algorithm and the inevitability of $\log|\mathcal{S}|$ in the regret bound.

ICLR Conference 2024 Conference Paper

How Many Pretraining Tasks Are Needed for In-Context Learning of Linear Regression?

• Jingfeng Wu
• Difan Zou
• Zixiang Chen
• Vladimir Braverman
• Quanquan Gu
• Peter L. Bartlett

Transformers pretrained on diverse tasks exhibit remarkable in-context learning (ICL) capabilities, enabling them to solve unseen tasks solely based on input contexts without adjusting model parameters. In this paper, we study ICL in one of its simplest setups: pretraining a single-layer linear attention model for linear regression with a Gaussian prior. We establish a statistical task complexity bound for the attention model pretraining, showing that effective pretraining only requires a small number of independent tasks. Furthermore, we prove that the pretrained model closely matches the Bayes optimal algorithm, i.e., optimally tuned ridge regression, by achieving nearly Bayes optimal risk on unseen tasks under a fixed context length. These theoretical findings complement prior experimental research and shed light on the statistical foundations of ICL.

NeurIPS Conference 2024 Conference Paper

Matching the Statistical Query Lower Bound for $k$-Sparse Parity Problems with Sign Stochastic Gradient Descent

• Yiwen Kou
• Zixiang Chen
• Quanquan Gu
• Sham M. Kakade

The $k$-sparse parity problem is a classical problem in computational complexity and algorithmic theory, serving as a key benchmark for understanding computational classes. In this paper, we solve the $k$-sparse parity problem with sign stochastic gradient descent, a variant of stochastic gradient descent (SGD) on two-layer fully-connected neural networks. We demonstrate that this approach can efficiently solve the $k$-sparse parity problem on a $d$-dimensional hypercube ($k\le O(\sqrt{d})$) with a sample complexity of $\tilde{O}(d^{k-1})$ using $2^{\Theta(k)}$ neurons, matching the established $\Omega(d^{k})$ lower bounds of Statistical Query (SQ) models. Our theoretical analysis begins by constructing a good neural network capable of correctly solving the $k$-parity problem. We then demonstrate how a trained neural network with sign SGD can effectively approximate this good network, solving the $k$-parity problem with small statistical errors. To the best of our knowledge, this is the first result that matches the SQ lower bound for solving $k$-sparse parity problem using gradient-based methods.

TMLR Journal 2024 Journal Article

On the Convergence of Adaptive Gradient Methods for Nonconvex Optimization

• Dongruo Zhou
• Jinghui Chen
• Yuan Cao
• Ziyan Yang
• Quanquan Gu

Adaptive gradient methods are workhorses in deep learning. However, the convergence guarantees of adaptive gradient methods for nonconvex optimization have not been thoroughly studied. In this paper, we provide a fine-grained convergence analysis for a general class of adaptive gradient methods including AMSGrad, RMSProp and AdaGrad. For smooth nonconvex functions, we prove that adaptive gradient methods in expectation converge to a first-order stationary point. Our convergence rate is better than existing results for adaptive gradient methods in terms of dimension. In addition, we also prove high probability bounds on the convergence rates of AMSGrad, RMSProp as well as AdaGrad, which have not been established before. Our analyses shed light on better understanding the mechanism behind adaptive gradient methods in optimizing nonconvex objectives.

ICLR Conference 2024 Conference Paper

Pessimistic Nonlinear Least-Squares Value Iteration for Offline Reinforcement Learning

• Qiwei Di
• Heyang Zhao
• Jiafan He
• Quanquan Gu

Offline reinforcement learning (RL), where the agent aims to learn the optimal policy based on the data collected by a behavior policy, has attracted increasing attention in recent years. While offline RL with linear function approximation has been extensively studied with optimal results achieved under certain assumptions, many works shift their interest to offline RL with non-linear function approximation. However, limited works on offline RL with non-linear function approximation have instance-dependent regret guarantees. In this paper, we propose an oracle-efficient algorithm, dubbed Pessimistic Nonlinear Least-Square Value Iteration (PNLSVI), for offline RL with non-linear function approximation. Our algorithmic design comprises three innovative components: (1) a variance-based weighted regression scheme that can be applied to a wide range of function classes, (2) a subroutine for variance estimation, and (3) a planning phase that utilizes a pessimistic value iteration approach. Our algorithm enjoys a regret bound that has a tight dependency on the function class complexity and achieves minimax optimal instance-dependent regret when specialized to linear function approximation. Our work extends the previous instance-dependent results within simpler function classes, such as linear and differentiable function to a more general framework. To the best of our knowledge, this is the first statistically optimal algorithm for nonlinear offline RL.

ICML Conference 2024 Conference Paper

Position: TrustLLM: Trustworthiness in Large Language Models

• Yue Huang 0001
• Lichao Sun 0001
• Haoran Wang 0005
• Siyuan Wu 0001
• Qihui Zhang
• Yuan Li
• Chujie Gao
• Yixin Huang

Large language models (LLMs) have gained considerable attention for their excellent natural language processing capabilities. Nonetheless, these LLMs present many challenges, particularly in the realm of trustworthiness. This paper introduces TrustLLM, a comprehensive study of trustworthiness in LLMs, including principles for different dimensions of trustworthiness, established benchmark, evaluation, and analysis of trustworthiness for mainstream LLMs, and discussion of open challenges and future directions. Specifically, we first propose a set of principles for trustworthy LLMs that span eight different dimensions. Based on these principles, we further establish a benchmark across six dimensions including truthfulness, safety, fairness, robustness, privacy, and machine ethics. We then present a study evaluating 16 mainstream LLMs in TrustLLM, consisting of over 30 datasets. Our findings firstly show that in general trustworthiness and capability (i. e. , functional effectiveness) are positively related. Secondly, our observations reveal that proprietary LLMs generally outperform most open-source counterparts in terms of trustworthiness, raising concerns about the potential risks of widely accessible open-source LLMs. However, a few open-source LLMs come very close to proprietary ones, suggesting that open-source models can achieve high levels of trustworthiness without additional mechanisms like moderator, offering valuable insights for developers in this field. Thirdly, it is important to note that some LLMs may be overly calibrated towards exhibiting trustworthiness, to the extent that they compromise their utility by mistakenly treating benign prompts as harmful and consequently not responding. Besides these observations, we’ve uncovered key insights into the multifaceted trustworthiness in LLMs. We emphasize the importance of ensuring transparency not only in the models themselves but also in the technologies that underpin trustworthiness. We advocate that the establishment of an AI alliance between industry, academia, the open-source community to foster collaboration is imperative to advance the trustworthiness of LLMs.

TMLR Journal 2024 Journal Article

Pre-trained Hypergraph Convolutional Neural Networks with Self-supervised Learning

• Yihe Deng
• Ruochi Zhang
• Pan Xu
• Jian Ma
• Quanquan Gu

Hypergraphs are powerful tools for modeling complex interactions across various domains, including biomedicine. However, learning meaningful node representations from hypergraphs remains a challenge. Existing supervised methods often lack generalizability, thereby limiting their real-world applications. We propose a new method, Pre-trained Hypergraph Convolutional Neural Networks with Self-supervised Learning (PhyGCN), which leverages hypergraph structure for self-supervision to enhance node representations. PhyGCN introduces a unique training strategy that integrates variable hyperedge sizes with self-supervised learning, enabling improved generalization to unseen data. Applications on multi-way chromatin interactions and polypharmacy side-effects demonstrate the effectiveness of PhyGCN. As a generic framework for high-order interaction datasets with abundant unlabeled data, PhyGCN holds strong potential for enhancing hypergraph node representations across various domains.

ICML Conference 2024 Conference Paper

Protein Conformation Generation via Force-Guided SE(3) Diffusion Models

• Yan Wang
• Lihao Wang
• Yuning Shen
• Yiqun Wang
• Huizhuo Yuan
• Yue Wu
• Quanquan Gu

The conformational landscape of proteins is crucial to understanding their functionality in complex biological processes. Traditional physics-based computational methods, such as molecular dynamics (MD) simulations, suffer from rare event sampling and long equilibration time problems, hindering their applications in general protein systems. Recently, deep generative modeling techniques, especially diffusion models, have been employed to generate novel protein conformations. However, existing score-based diffusion methods cannot properly incorporate important physical prior knowledge to guide the generation process, causing large deviations in the sampled protein conformations from the equilibrium distribution. In this paper, to overcome these limitations, we propose a force-guided $\mathrm{SE}(3)$ diffusion model, ConfDiff, for protein conformation generation. By incorporating a force-guided network with a mixture of data-based score models, ConfDiff can generate protein conformations with rich diversity while preserving high fidelity. Experiments on a variety of protein conformation prediction tasks, including 12 fast-folding proteins and the Bovine Pancreatic Trypsin Inhibitor (BPTI), demonstrate that our method surpasses the state-of-the-art method.

UAI Conference 2024 Conference Paper

Pure Exploration in Asynchronous Federated Bandits

• Zichen Wang
• Chuanhao Li 0002
• Chenyu Song
• Lianghui Wang
• Quanquan Gu
• Huazheng Wang

We study the federated pure exploration problem of multi-armed bandits and linear bandits, where $M$ agents cooperatively identify the best arm via communicating with the central server. To enhance the robustness against latency and unavailability of agents that are common in practice, we propose the first federated asynchronous multi-armed bandit and linear bandit algorithms for pure exploration with fixed confidence. Our theoretical analysis shows the proposed algorithms achieve near-optimal sample complexities and efficient communication costs in a fully asynchronous environment. Moreover, experimental results based on synthetic and real-world data empirically elucidate the effectiveness and communication cost-efficiency of the proposed algorithms.

ICLR Conference 2024 Conference Paper

Risk Bounds of Accelerated SGD for Overparameterized Linear Regression

• Xuheng Li
• Yihe Deng
• Jingfeng Wu
• Dongruo Zhou
• Quanquan Gu

Accelerated stochastic gradient descent (ASGD) is a workhorse in deep learning and often achieves better generalization performance than SGD. However, existing optimization theory can only explain the faster convergence of ASGD, but cannot explain its better generalization. In this paper, we study the generalization of ASGD for overparameterized linear regression, which is possibly the simplest setting of learning with overparameterization. We establish an instance-dependent excess risk bound for ASGD within each eigen-subspace of the data covariance matrix. Our analysis shows that (i) ASGD outperforms SGD in the subspace of small eigenvalues, exhibiting a faster rate of exponential decay for bias error, while in the subspace of large eigenvalues, its bias error decays slower than SGD; and (ii) the variance error of ASGD is always larger than that of SGD. Our result suggests that ASGD can outperform SGD when the difference between the initialization and the true weight vector is mostly confined to the subspace of small eigenvalues. Additionally, when our analysis is specialized to linear regression in the strongly convex setting, it yields a tighter bound for bias error than the best-known result.

ICML Conference 2024 Conference Paper

Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models

• Zixiang Chen
• Yihe Deng
• Huizhuo Yuan
• Kaixuan Ji
• Quanquan Gu

Harnessing the power of human-annotated data through Supervised Fine-Tuning (SFT) is pivotal for advancing Large Language Models (LLMs). In this paper, we delve into the prospect of growing a strong LLM out of a weak one without the need for acquiring additional human-annotated data. We propose a new fine-tuning method called Self-Play fIne-tuNing (SPIN), which starts from a supervised fine-tuned model. At the heart of SPIN lies a self-play mechanism, where the LLM refines its capability by playing against instances of itself. More specifically, the LLM generates its own training data from its previous iterations, refining its policy by discerning these self-generated responses from those obtained from human-annotated data. Our method progressively elevates the LLM from a nascent model to a formidable one, unlocking the full potential of human-annotated demonstration data for SFT. Theoretically, we prove that the global optimum to the training objective function of our method is achieved only when the LLM policy aligns with the target data distribution. Empirically, we evaluate our method on several benchmark datasets including the HuggingFace Open LLM Leaderboard, MT-Bench, and datasets from Big-Bench. Our results show that SPIN can significantly improve the LLM’s performance across a variety of benchmarks and even outperform models trained through direct preference optimization (DPO) supplemented with extra GPT-4 preference data. This sheds light on the promise of self-play, enabling the achievement of human-level performance in LLMs without the need for expert opponents.

NeurIPS Conference 2024 Conference Paper

Self-Play Fine-tuning of Diffusion Models for Text-to-image Generation

• Huizhuo Yuan
• Zixiang Chen
• Kaixuan Ji
• Quanquan Gu

Fine-tuning Diffusion Models remains an underexplored frontier in generative artificial intelligence (GenAI), especially when compared with the remarkable progress made in fine-tuning Large Language Models (LLMs). While cutting-edge diffusion models such as Stable Diffusion (SD) and SDXL rely on supervised fine-tuning, their performance inevitably plateaus after seeing a certain volume of data. Recently, reinforcement learning (RL) has been employed to fine-tune diffusion models with human preference data, but it requires at least two images ( winner'' and loser'' images) for each text prompt. In this paper, we introduce an innovative technique called self-play fine-tuning for diffusion models (SPIN-Diffusion), where the diffusion model engages in competition with its earlier versions, facilitating an iterative self-improvement process. Our approach offers an alternative to conventional supervised fine-tuning and RL strategies, significantly improving both model performance and alignment. Our experiments on the Pick-a-Pic dataset reveal that SPIN-Diffusion outperforms the existing supervised fine-tuning method in aspects of human preference alignment and visual appeal right from its first iteration. By the second iteration, it exceeds the performance of RLHF-based methods across all metrics, achieving these results with less data. Codes are available at \url{https: //github. com/uclaml/SPIN-Diffusion/}.

ICML Conference 2024 Conference Paper

Towards Robust Model-Based Reinforcement Learning Against Adversarial Corruption

• Chenlu Ye
• Jiafan He
• Quanquan Gu
• Tong Zhang 0001

This study tackles the challenges of adversarial corruption in model-based reinforcement learning (RL), where the transition dynamics can be corrupted by an adversary. Existing studies on corruption-robust RL mostly focus on the setting of model-free RL, where robust least-square regression is often employed for value function estimation. However, these techniques cannot be directly applied to model-based RL. In this paper, we focus on model-based RL and take the maximum likelihood estimation (MLE) approach to learn transition model. Our work encompasses both online and offline settings. In the online setting, we introduce an algorithm called corruption-robust optimistic MLE (CR-OMLE), which leverages total-variation (TV)-based information ratios as uncertainty weights for MLE. We prove that CR-OMLE achieves a regret of $\tilde{\mathcal{O}}(\sqrt{T} + C)$, where $C$ denotes the cumulative corruption level after $T$ episodes. We also prove a lower bound to show that the additive dependence on $C$ is optimal. We extend our weighting technique to the offline setting, and propose an algorithm named corruption-robust pessimistic MLE (CR-PMLE). Under a uniform coverage condition, CR-PMLE exhibits suboptimality worsened by $\mathcal{O}(C/n)$, nearly matching the lower bound. To the best of our knowledge, this is the first work on corruption-robust model-based RL algorithms with provable guarantees.

ICML Conference 2024 Conference Paper

Uncertainty-Aware Reward-Free Exploration with General Function Approximation

• Junkai Zhang
• Weitong Zhang
• Dongruo Zhou
• Quanquan Gu

Mastering multiple tasks through exploration and learning in an environment poses a significant challenge in reinforcement learning (RL). Unsupervised RL has been introduced to address this challenge by training policies with intrinsic rewards rather than extrinsic rewards. However, current intrinsic reward designs and unsupervised RL algorithms often overlook the heterogeneous nature of collected samples, thereby diminishing their sample efficiency. To overcome this limitation, in this paper, we proposed a reward-free RL algorithm called GFA-RFE. The key idea behind our algorithm is an uncertainty-aware intrinsic reward for exploring the environment and an uncertainty-weighted learning process to handle heterogeneous uncertainty in different samples. Theoretically, we show that in order to find an $\epsilon$-optimal policy, GFA-RFE needs to collect $\tilde{O} (H^2 \log N_{\mathcal{F}} (\epsilon) \text{dim} (\mathcal{F}) / \epsilon^2 )$ number of episodes, where $\mathcal{F}$ is the value function class with covering number $N_{\mathcal{F}} (\epsilon)$ and generalized eluder dimension $\text{dim} (\mathcal{F})$. Such a result outperforms all existing reward-free RL algorithms. We further implement and evaluate GFA-RFE across various domains and tasks in the DeepMind Control Suite. Experiment results show that GFA-RFE outperforms or is comparable to the performance of state-of-the-art unsupervised RL algorithms.

ICLR Conference 2024 Conference Paper

Understanding Transferable Representation Learning and Zero-shot Transfer in CLIP

• Zixiang Chen
• Yihe Deng
• Yuanzhi Li
• Quanquan Gu

Multi-modal learning has become increasingly popular due to its ability to leverage information from different data sources (e.g., text and images) to improve the model performance. Recently, CLIP has emerged as an effective approach that employs vision-language contrastive pretraining to learn joint image and text representations and exhibits remarkable performance in zero-shot learning and text-guided natural image generation. Despite the substantial practical success of CLIP, its theoretical understanding remains elusive. In this paper, we formally study transferrable representation learning underlying CLIP and demonstrate how features from different modalities get aligned. We also analyze its zero-shot transfer performance on the downstream tasks. In addition, we conduct empirical evaluations on real data to back up our theory. Inspired by our analysis, we propose a new CLIP-type approach, which achieves better performance than CLIP and other state-of-the-art methods on benchmark datasets.

ICLR Conference 2024 Conference Paper

Variance-aware Regret Bounds for Stochastic Contextual Dueling Bandits

• Qiwei Di
• Tao Jin 0002
• Yue Wu
• Heyang Zhao
• Farzad Farnoud
• Quanquan Gu

Dueling bandits is a prominent framework for decision-making involving preferential feedback, a valuable feature that fits various applications involving human interaction, such as ranking, information retrieval, and recommendation systems. While substantial efforts have been made to minimize the cumulative regret in dueling bandits, a notable gap in the current research is the absence of regret bounds that account for the inherent uncertainty in pairwise comparisons between the dueling arms. Intuitively, greater uncertainty suggests a higher level of difficulty in the problem. To bridge this gap, this paper studies the problem of contextual dueling bandits, where the binary comparison of dueling arms is generated from a generalized linear model (GLM). We propose a new SupLinUCB-type algorithm that enjoys computational efficiency and a variance-aware regret bound $\tilde O\big(d\sqrt{\sum_{t=1}^T\sigma_t^2} + d\big)$, where $\sigma_t$ is the variance of the pairwise comparison at round $t$, $d$ is the dimension of the context vectors, and $T$ is the time horizon. Our regret bound naturally aligns with the intuitive expectation — in scenarios where the comparison is deterministic, the algorithm only suffers from an $\tilde O(d)$ regret. We perform empirical experiments on synthetic data to confirm the advantage of our method over previous variance-agnostic algorithms.

ICLR Conference 2023 Conference Paper

A General Framework for Sample-Efficient Function Approximation in Reinforcement Learning

• Zixiang Chen
• Chris Junchi Li
• Huizhuo Yuan
• Quanquan Gu
• Michael I. Jordan

With the increasing need for handling large state and action spaces, general function approximation has become a key technique in reinforcement learning (RL). In this paper, we propose a general framework that unifies model-based and model-free RL, and an Admissible Bellman Characterization (ABC) class that subsumes nearly all Markov decision process (MDP) models in the literature for tractable RL. We propose a novel estimation function with decomposable structural properties for optimization-based exploration and the functional Eluder dimension as a complexity measure of the ABC class. Under our framework, a new sample-efficient algorithm namely OPtimization-based ExploRation with Approximation (OPERA) is proposed, achieving regret bounds that match or improve over the best-known results for a variety of MDP models. In particular, for MDPs with low Witness rank, under a slightly stronger assumption, OPERA improves the state-of-the-art sample complexity results by a factor of $dH$. Our framework provides a generic interface to design and analyze new RL models and algorithms.

UAI Conference 2023 Conference Paper

Benign Overfitting in Adversarially Robust Linear Classification

• Jinghui Chen
• Yuan Cao 0006
• Quanquan Gu

Benign overfitting, where classifiers memorize noisy training data yet still achieve a good generalization performance, has drawn great attention in the machine learning community. To explain this surprising phenomenon, a series of works have provided theoretical justification for over-parameterized linear regression, classification, and kernel methods. However, it is not clear if benign overfitting can occur in the presence of adversarial examples, i. e. , examples with tiny and intentional perturbations to fool the classifiers. In this paper, we show that benign overfitting indeed occurs in adversarial training, a principled approach to defend against adversarial examples, on subGaussian mixture data. In detail, we prove the risk bounds of the adversarially trained linear classifier on the mixture of sub-Gaussian data under Lp adversarial perturbations. Our result suggests that under moderate perturbations, adversarially trained linear classifiers can achieve the near-optimal standard and adversarial risks, despite overfitting the noisy training data. Numerical experiments validate our theoretical findings.

ICML Conference 2023 Conference Paper

Benign Overfitting in Two-layer ReLU Convolutional Neural Networks

• Yiwen Kou
• Zixiang Chen
• Yuanzhou Chen
• Quanquan Gu

Modern deep learning models with great expressive power can be trained to overfit the training data but still generalize well. This phenomenon is referred to as benign overfitting. Recently, a few studies have attempted to theoretically understand benign overfitting in neural networks. However, these works are either limited to neural networks with smooth activation functions or to the neural tangent kernel regime. How and when benign overfitting can occur in ReLU neural networks remains an open problem. In this work, we seek to answer this question by establishing algorithm-dependent risk bounds for learning two-layer ReLU convolutional neural networks with label-flipping noise. We show that, under mild conditions, the neural network trained by gradient descent can achieve near-zero training loss and Bayes optimal test risk. Our result also reveals a sharp transition between benign and harmful overfitting under different conditions on data distribution in terms of test risk. Experiments on synthetic data back up our theory.

JMLR Journal 2023 Journal Article

Benign Overfitting of Constant-Stepsize SGD for Linear Regression

• Difan Zou
• Jingfeng Wu
• Vladimir Braverman
• Quanquan Gu
• Sham M. Kakade

There is an increasing realization that algorithmic inductive biases are central in preventing overfitting; empirically, we often see a benign overfitting phenomenon in overparameterized settings for natural learning algorithms, such as stochastic gradient descent (SGD), where little to no explicit regularization has been employed. This work considers this issue in arguably the most basic setting: constant-stepsize SGD (with iterate averaging or tail averaging) for linear regression in the overparameterized regime. Our main result provides a sharp excess risk bound, stated in terms of the full eigenspectrum of the data covariance matrix, that reveals a bias-variance decomposition characterizing when generalization is possible: (i) the variance bound is characterized in terms of an effective dimension (specific for SGD) and (ii) the bias bound provides a sharp geometric characterization in terms of the location of the initial iterate (and how it aligns with the data covariance matrix). More specifically, for SGD with iterate averaging, we demonstrate the sharpness of the established excess risk bound by proving a matching lower bound (up to constant factors). For SGD with tail averaging, we show its advantage over SGD with iterate averaging by proving a better excess risk bound together with a nearly matching lower bound. Moreover, we reflect on a number of notable differences between the algorithmic regularization afforded by (unregularized) SGD in comparison to ordinary least squares (minimum-norm interpolation) and ridge regression. Experimental results on synthetic data corroborate our theoretical findings. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

ICML Conference 2023 Conference Paper

Cooperative Multi-Agent Reinforcement Learning: Asynchronous Communication and Linear Function Approximation

• Yifei Min
• Jiafan He
• Tianhao Wang 0002
• Quanquan Gu

We study multi-agent reinforcement learning in the setting of episodic Markov decision processes, where many agents cooperate via communication through a central server. We propose a provably efficient algorithm based on value iteration that can simultaneously allow asynchronous communication and guarantee the benefit of cooperation with low communication complexity. Under linear function approximation, we prove that our algorithm enjoys a $\tilde{\mathcal{O}}(d^{3/2}H^2\sqrt{K})$ regret upper bound with $\tilde{\mathcal{O}}(dHM^2)$ communication complexity, where $d$ is the feature dimension, $H$ is the horizon length, $M$ is the total number of agents, and $K$ is the total number of episodes. We also provide a lower bound showing that an $\Omega(dM)$ communication complexity is necessary to improve the performance through collaboration.

ICML Conference 2023 Conference Paper

Corruption-Robust Algorithms with Uncertainty Weighting for Nonlinear Contextual Bandits and Markov Decision Processes

• Chenlu Ye
• Wei Xiong 0015
• Quanquan Gu
• Tong Zhang 0001

Despite the significant interest and progress in reinforcement learning (RL) problems with adversarial corruption, current works are either confined to the linear setting or lead to an undesired $\tilde{\mathcal O}(\sqrt{T}\zeta)$ regret bound, where $T$ is the number of rounds and $\zeta$ is the total amount of corruption. In this paper, we consider contextual bandits with general function approximation and propose a computationally efficient algorithm to achieve a regret of $\tilde{\mathcal O}(\sqrt{T}+\zeta)$. The proposed algorithm relies on the recently developed uncertainty-weighted least-squares regression from linear contextual bandits (He et al. , 2022) and a new weighted estimator of uncertainty for the general function class. In contrast to the existing analysis for the sum of uncertainty that is heavily based on the linear structure, we develop a novel technique to control the sum of weighted uncertainty, thus establishing the final regret bound. We then generalize our algorithm to the episodic MDP and first achieve an additive dependence on the corruption level $\zeta$ in the scenario of general function approximation. Notably, our algorithms achieve regret bounds that either nearly match the lower bound or improve the performance of existing methods for all the corruption levels in both known and unknown $\zeta$ cases.

NeurIPS Conference 2023 Conference Paper

Corruption-Robust Offline Reinforcement Learning with General Function Approximation

• Chenlu Ye
• Rui Yang
• Quanquan Gu
• Tong Zhang

We investigate the problem of corruption robustness in offline reinforcement learning (RL) with general function approximation, where an adversary can corrupt each sample in the offline dataset, and the corruption level $\zeta\geq0$ quantifies the cumulative corruption amount over $n$ episodes and $H$ steps. Our goal is to find a policy that is robust to such corruption and minimizes the suboptimality gap with respect to the optimal policy for the uncorrupted Markov decision processes (MDPs). Drawing inspiration from the uncertainty-weighting technique from the robust online RL setting \citep{he2022nearly, ye2022corruptionrobust}, we design a new uncertainty weight iteration procedure to efficiently compute on batched samples and propose a corruption-robust algorithm for offline RL. Notably, under the assumption of single policy coverage and the knowledge of $\zeta$, our proposed algorithm achieves a suboptimality bound that is worsened by an additive factor of $\mathcal O(\zeta \cdot (\text CC(\lambda, \hat{\mathcal F}, \mathcal Z_n^H))^{1/2} (C(\hat{\mathcal F}, \mu))^{-1/2} n^{-1})$ due to the corruption. Here $\text CC(\lambda, \hat{\mathcal F}, \mathcal Z_n^H)$ is the coverage coefficient that depends on the regularization parameter $\lambda$, the confidence set $\hat{\mathcal F}$, and the dataset $\mathcal Z_n^H$, and $C(\hat{\mathcal F}, \mu)$ is a coefficient that depends on $\hat{\mathcal F}$ and the underlying data distribution $\mu$. When specialized to linear MDPs, the corruption-dependent error term reduces to $\mathcal O(\zeta d n^{-1})$ with $d$ being the dimension of the feature map, which matches the existing lower bound for corrupted linear MDPs. This suggests that our analysis is tight in terms of the corruption-dependent term.

ICML Conference 2023 Conference Paper

DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design

• Jiaqi Guan
• Xiangxin Zhou
• Yuwei Yang
• Yu Bao
• Jian Peng 0001
• Jianzhu Ma
• Qiang Liu 0006
• Liang Wang 0001

Designing 3D ligands within a target binding site is a fundamental task in drug discovery. Existing structured-based drug design methods treat all ligand atoms equally, which ignores different roles of atoms in the ligand for drug design and can be less efficient for exploring the large drug-like molecule space. In this paper, inspired by the convention in pharmaceutical practice, we decompose the ligand molecule into two parts, namely arms and scaffold, and propose a new diffusion model, DecompDiff, with decomposed priors over arms and scaffold. In order to facilitate the decomposed generation and improve the properties of the generated molecules, we incorporate both bond diffusion in the model and additional validity guidance in the sampling phase. Extensive experiments on CrossDocked2020 show that our approach achieves state-of-the-art performance in generating high-affinity molecules while maintaining proper molecular properties and conformational stability, with up to $-8. 39$ Avg. Vina Dock score and $24. 5%$ Success Rate. The code is provided at https: //github. com/bytedance/DecompDiff

UAI Conference 2023 Conference Paper

Efficient Privacy-Preserving Stochastic Nonconvex Optimization

• Lingxiao Wang 0001
• Bargav Jayaraman
• David Evans 0001
• Quanquan Gu

While many solutions for privacy-preserving convex empirical risk minimization (ERM) have been developed, privacy-preserving nonconvex ERM remains a challenge. We study nonconvex ERM, which takes the form of minimizing a finite-sum of nonconvex loss functions over a training set. We propose a new differentially private stochastic gradient descent algorithm for nonconvex ERM that achieves strong privacy guarantees efficiently, and provide a tight analysis of its privacy and utility guarantees, as well as its gradient complexity. Our algorithm reduces gradient complexity while matching the best-known utility guarantee. Our experiments on benchmark nonconvex ERM problems demonstrate superior performance in terms of both training cost and utility gains compared with previous differentially private methods using the same privacy budgets.

ICML Conference 2023 Conference Paper

Finite-Sample Analysis of Learning High-Dimensional Single ReLU Neuron

• Jingfeng Wu
• Difan Zou
• Zixiang Chen
• Vladimir Braverman
• Quanquan Gu
• Sham M. Kakade

This paper considers the problem of learning single ReLU neuron with squared loss (a. k. a. , ReLU regression) in the overparameterized regime, where the input dimension can exceed the number of samples. We analyze a Perceptron-type algorithm called GLM-tron [Kakade et al. 2011], and provide its dimension-free risk upper bounds for high-dimensional ReLU regression in both well-specified and misspecified settings. Our risk bounds recover several existing results as special cases. Moreover, in the well-specified setting, we also provide an instance-wise matching risk lower bound for GLM-tron. Our upper and lower risk bounds provide a sharp characterization of the high-dimensional ReLU regression problems that can be learned via GLM-tron. On the other hand, we provide some negative results for stochastic gradient descent (SGD) for ReLU regression with symmetric Bernoulli data: if the model is well-specified, the excess risk of SGD is provably no better than that of GLM-tron ignoring constant factors, for each problem instance; and in the noiseless case, GLM-tron can achieve a small risk while SGD unavoidably suffers from a constant risk in expectation. These results together suggest that GLM-tron might be more preferable than SGD for high-dimensional ReLU regression.

ICLR Conference 2023 Conference Paper

How Does Semi-supervised Learning with Pseudo-labelers Work? A Case Study

• Yiwen Kou
• Zixiang Chen
• Yuan Cao 0006
• Quanquan Gu

Semi-supervised learning is a popular machine learning paradigm that utilizes a large amount of unlabeled data as well as a small amount of labeled data to facilitate learning tasks. While semi-supervised learning has achieved great success in training neural networks, its theoretical understanding remains largely open. In this paper, we aim to theoretically understand a semi-supervised learning approach based on pre-training and linear probing. In particular, the semi-supervised learning approach we consider first trains a two-layer neural network based on the unlabeled data with the help of pseudo-labelers. Then it linearly probes the pre-trained network on a small amount of labeled data. We prove that, under a certain toy data generation model and two-layer convolutional neural network, the semisupervised learning approach can achieve nearly zero test loss, while a neural network directly trained by supervised learning on the same amount of labeled data can only achieve constant test loss. Through this case study, we demonstrate a separation between semi-supervised learning and supervised learning in terms of test loss provided the same amount of labeled data.

NeurIPS Conference 2023 Conference Paper

Implicit Bias of Gradient Descent for Two-layer ReLU and Leaky ReLU Networks on Nearly-orthogonal Data

• Yiwen Kou
• Zixiang Chen
• Quanquan Gu

The implicit bias towards solutions with favorable properties is believed to be a key reason why neural networks trained by gradient-based optimization can generalize well. While the implicit bias of gradient flow has been widely studied for homogeneous neural networks (including ReLU and leaky ReLU networks), the implicit bias of gradient descent is currently only understood for smooth neural networks. Therefore, implicit bias in non-smooth neural networks trained by gradient descent remains an open question. In this paper, we aim to answer this question by studying the implicit bias of gradient descent for training two-layer fully connected (leaky) ReLU neural networks. We showed that when the training data are nearly-orthogonal, for leaky ReLU activation function, gradient descent will find a network with a stable rank that converges to $1$, whereas for ReLU activation function, gradient descent will find a neural network with a stable rank that is upper bounded by a constant. Additionally, we show that gradient descent will find a neural network such that all the training data points have the same normalized margin asymptotically. Experiments on both synthetic and real data backup our theoretical findings.

ICML Conference 2023 Conference Paper

Nearly Minimax Optimal Regret for Learning Linear Mixture Stochastic Shortest Path

• Qiwei Di
• Jiafan He
• Dongruo Zhou
• Quanquan Gu

We study the Stochastic Shortest Path (SSP) problem with a linear mixture transition kernel, where an agent repeatedly interacts with a stochastic environment and seeks to reach certain goal state while minimizing the cumulative cost. Existing works often assume a strictly positive lower bound of the cost function or an upper bound of the expected length for the optimal policy. In this paper, we propose a new algorithm to eliminate these restrictive assumptions. Our algorithm is based on extended value iteration with a fine-grained variance-aware confidence set, where the variance is estimated recursively from high-order moments. Our algorithm achieves an $\tilde{\mathcal{O}}(dB_*\sqrt{K})$ regret bound, where $d$ is the dimension of the feature mapping in the linear transition kernel, $B_*$ is the upper bound of the total cumulative cost for the optimal policy, and $K$ is the number of episodes. Our regret upper bound matches the $\Omega(dB_*\sqrt{K})$ lower bound of linear mixture SSPs in Min et al. (2022), which suggests that our algorithm is nearly minimax optimal.

ICML Conference 2023 Conference Paper

Nearly Minimax Optimal Reinforcement Learning for Linear Markov Decision Processes

• Jiafan He
• Heyang Zhao
• Dongruo Zhou
• Quanquan Gu

We study reinforcement learning (RL) with linear function approximation. For episodic time-inhomogeneous linear Markov decision processes (linear MDPs) whose transition probability can be parameterized as a linear function of a given feature mapping, we propose the first computationally efficient algorithm that achieves the nearly minimax optimal regret $\tilde O(d\sqrt{H^3K})$, where $d$ is the dimension of the feature mapping, $H$ is the planning horizon, and $K$ is the number of episodes. Our algorithm is based on a weighted linear regression scheme with a carefully designed weight, which depends on a new variance estimator that (1) directly estimates the variance of the optimal value function, (2) monotonically decreases with respect to the number of episodes to ensure a better estimation accuracy, and (3) uses a rare-switching policy to update the value function estimator to control the complexity of the estimated value function class. Our work provides a complete answer to optimal RL with linear MDPs, and the developed algorithm and theoretical tools may be of independent interest.

ICML Conference 2023 Conference Paper

Nesterov Meets Optimism: Rate-Optimal Separable Minimax Optimization

• Chris Junchi Li
• Huizhuo Yuan
• Gauthier Gidel
• Quanquan Gu
• Michael I. Jordan

We propose a new first-order optimization algorithm — AcceleratedGradient-OptimisticGradient (AG-OG) Descent Ascent—for separable convex-concave minimax optimization. The main idea of our algorithm is to carefully leverage the structure of the minimax problem, performing Nesterov acceleration on the individual component and optimistic gradient on the coupling component. Equipped with proper restarting, we show that AG-OG achieves the optimal convergence rate (up to a constant) for a variety of settings, including bilinearly coupled strongly convex-strongly concave minimax optimization (bi-SC-SC), bilinearly coupled convex-strongly concave minimax optimization (bi-C-SC), and bilinear games. We also extend our algorithm to the stochastic setting and achieve the optimal convergence rate in both bi-SC-SC and bi-C-SC settings. AG-OG is the first single-call algorithm with optimal convergence rates in both deterministic and stochastic settings for bilinearly coupled minimax optimization problems.

ICML Conference 2023 Conference Paper

On the Interplay Between Misspecification and Sub-optimality Gap in Linear Contextual Bandits

• Weitong Zhang
• Jiafan He
• Zhiyuan Fan
• Quanquan Gu

We study linear contextual bandits in the misspecified setting, where the expected reward function can be approximated by a linear function class up to a bounded misspecification level $\zeta>0$. We propose an algorithm based on a novel data selection scheme, which only selects the contextual vectors with large uncertainty for online regression. We show that, when the misspecification level $\zeta$ is dominated by $\tilde O(\Delta / \sqrt{d})$ with $\Delta$ being the minimal sub-optimality gap and $d$ being the dimension of the contextual vectors, our algorithm enjoys the same gap-dependent regret bound $\tilde O ({d^2} /{\Delta})$ as in the well-specified setting up to logarithmic factors. Given this result, we show that the existing SupLinUCB algorithm (Chu et al. , 2011) can also achieve a gap-dependent constant regret bound without the knowledge of sub-optimality gap $\Delta$. Together with a lower bound adapted from Lattimore et al. (2020), our result suggests an interplay between the misspecification level and the sub-optimality gap: (1) the linear contextual bandit model is efficiently learnable when $\zeta \leq \tilde O({\Delta} / \sqrt{d})$; and (2) it is not efficiently learnable when $\zeta \geq \tilde \Omega({\Delta} / {\sqrt{d}})$. Experiments on both synthetic and real-world datasets corroborate our theoretical results.

NeurIPS Conference 2023 Conference Paper

Optimal Extragradient-Based Algorithms for Stochastic Variational Inequalities with Separable Structure

• Angela Yuan
• Chris Junchi Li
• Gauthier Gidel
• Michael Jordan
• Quanquan Gu
• Simon S. Du

We consider the problem of solving stochastic monotone variational inequalities with a separable structure using a stochastic first-order oracle. Building on standard extragradient for variational inequalities we propose a novel algorithm---stochastic \emph{accelerated gradient-extragradient} (AG-EG)---for strongly monotone variational inequalities (VIs). Our approach combines the strengths of extragradient and Nesterov acceleration. By showing that its iterates remain in a bounded domain and applying scheduled restarting, we prove that AG-EG has an optimal convergence rate for strongly monotone VIs. Furthermore, when specializing to the particular case of bilinearly coupled strongly-convex-strongly-concave saddle-point problems, including bilinear games, our algorithm achieves fine-grained convergence rates that match the respective lower bounds, with the stochasticity being characterized by an additive statistical error term that is optimal up to a constant prefactor.

ICML Conference 2023 Conference Paper

Optimal Horizon-Free Reward-Free Exploration for Linear Mixture MDPs

• Junkai Zhang
• Weitong Zhang
• Quanquan Gu

We study reward-free reinforcement learning (RL) with linear function approximation, where the agent works in two phases: (1) in the exploration phase, the agent interacts with the environment but cannot access the reward; and (2) in the planning phase, the agent is given a reward function and is expected to find a near-optimal policy based on samples collected in the exploration phase. The sample complexities of existing reward-free algorithms have a polynomial dependence on the planning horizon, which makes them intractable for long planning horizon RL problems. In this paper, we propose a new reward-free algorithm for learning linear mixture Markov decision processes (MDPs), where the transition probability can be parameterized as a linear combination of known feature mappings. At the core of our algorithm is uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward and a high-order moment estimator for the aleatoric and epistemic uncertainties. When the total reward is bounded by $1$, we show that our algorithm only needs to explore $\tilde O\left( d^2\varepsilon^{-2}\right)$ episodes to find an $\varepsilon$-optimal policy, where $d$ is the dimension of the feature mapping. The sample complexity of our algorithm only has a polylogarithmic dependence on the planning horizon and therefore is "horizon-free”. In addition, we provide an $\Omega\left(d^2\varepsilon^{-2}\right)$ sample complexity lower bound, which matches the sample complexity of our algorithm up to logarithmic factors, suggesting that our algorithm is optimal.

ICML Conference 2023 Conference Paper

Optimal Online Generalized Linear Regression with Stochastic Noise and Its Application to Heteroscedastic Bandits

• Heyang Zhao
• Dongruo Zhou
• Jiafan He
• Quanquan Gu

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical follow-the-regularized-leader (FTRL) algorithm to cope with the label noise. More specifically, for $\sigma$-sub-Gaussian label noise, our analysis provides a regret upper bound of $O(\sigma^2 d \log T) + o(\log T)$, where $d$ is the dimension of the input vector, $T$ is the total number of rounds. We also prove an $\Omega(\sigma^2d\log(T/d))$ lower bound for stochastic online linear regression, which indicates that our upper bound is nearly optimal. In addition, we extend our analysis to a more refined Bernstein noise condition. As an application, we study generalized linear bandits with heterogeneous noise and propose an algorithm based on FTRL to achieve the first variance-aware regret bound.

ICML Conference 2023 Conference Paper

Personalized Federated Learning under Mixture of Distributions

• Yue Wu
• Shuaicheng Zhang
• Wenchao Yu
• Yanchi Liu
• Quanquan Gu
• Dawei Zhou 0003
• Haifeng Chen
• Wei Cheng 0002

The recent trend towards Personalized Federated Learning (PFL) has garnered significant attention as it allows for the training of models that are tailored to each client while maintaining data privacy. However, current PFL techniques primarily focus on modeling the conditional distribution heterogeneity (i. e. concept shift), which can result in suboptimal performance when the distribution of input data across clients diverges (i. e. covariate shift). Additionally, these techniques often lack the ability to adapt to unseen data, further limiting their effectiveness in real-world scenarios. To address these limitations, we propose a novel approach, FedGMM, which utilizes Gaussian mixture models (GMM) to effectively fit the input data distributions across diverse clients. The model parameters are estimated by maximum likelihood estimation utilizing a federated Expectation-Maximization algorithm, which is solved in closed form and does not assume gradient similarity. Furthermore, FedGMM possesses an additional advantage of adapting to new clients with minimal overhead, and it also enables uncertainty quantification. Empirical evaluations on synthetic and benchmark datasets demonstrate the superior performance of our method in both PFL classification and novel sample detection.

UAI Conference 2023 Conference Paper

Provably efficient representation selection in Low-rank Markov Decision Processes: from online to offline RL

• Weitong Zhang
• Jiafan He
• Dongruo Zhou
• Amy Zhang 0001
• Quanquan Gu

The success of deep reinforcement learning (DRL) lies in its ability to learn a representation that is well-suited for the exploration and exploitation task. To understand how the choice of representation can improve the efficiency of reinforcement learning (RL), we study representation selection for a class of low-rank Markov Decision Processes (MDPs) where the transition kernel can be represented in a bilinear form. We propose an efficient algorithm, called ReLEX, for representation learning in both online and offline RL. Specifically, we show that the online version of ReLEX, called ReLEX-UCB, always performs no worse than the state-of-the-art algorithm without representation selection, and achieves a strictly better constant regret if the representation function class has a "coverage" property over the entire state-action space. For the offline counterpart, ReLEX-LCB, we show that the algorithm can find the optimal policy if the representation class can cover the state-action space and achieves gap-dependent sample complexity. This is the first result with constant sample complexity for representation learning in offline RL.

NeurIPS Conference 2023 Conference Paper

Robust Learning with Progressive Data Expansion Against Spurious Correlation

• Yihe Deng
• Yu Yang
• Baharan Mirzasoleiman
• Quanquan Gu

While deep learning models have shown remarkable performance in various tasks, they are susceptible to learning non-generalizable _spurious features_ rather than the core features that are genuinely correlated to the true label. In this paper, beyond existing analyses of linear models, we theoretically examine the learning process of a two-layer nonlinear convolutional neural network in the presence of spurious features. Our analysis suggests that imbalanced data groups and easily learnable spurious features can lead to the dominance of spurious features during the learning process. In light of this, we propose a new training algorithm called **PDE** that efficiently enhances the model's robustness for a better worst-group performance. PDE begins with a group-balanced subset of training data and progressively expands it to facilitate the learning of the core features. Experiments on synthetic and real-world benchmark datasets confirm the superior performance of our method on models such as ResNets and Transformers. On average, our method achieves a $2. 8$ \% improvement in worst-group accuracy compared with the state-of-the-art method, while enjoying up to $10\times$ faster training efficiency.

ICML Conference 2023 Conference Paper

Structure-informed Language Models Are Protein Designers

• Zaixiang Zheng
• Yifan Deng
• Dongyu Xue
• Yi Zhou 0018
• Fei Ye
• Quanquan Gu

This paper demonstrates that language models are strong structure-based protein designers. We present LM-Design, a generic approach to reprogramming sequence-based protein language models (pLMs), that have learned massive sequential evolutionary knowledge from the universe of natural protein sequences, to acquire an immediate capability to design preferable protein sequences for given folds. We conduct a structural surgery on pLMs, where a lightweight structural adapter is implanted into pLMs and endows it with structural awareness. During inference, iterative refinement is performed to effectively optimize the generated protein sequences. Experiments show that LM-Design improves the state-of-the-art results by a large margin, leading to 4% to 12% accuracy gains in sequence recovery (e. g. , 55. 65%/56. 63% on CATH 4. 2/4. 3 single-chain benchmarks, and $>$60% when designing protein complexes). We provide extensive and in-depth analyses, which verify that LM-Design can (1) indeed leverage both structural and sequential knowledge to accurately handle structurally non-deterministic regions, (2) benefit from scaling data and model size, and (3) generalize to other proteins (e. g. , antibodies and de novo proteins).

ICML Conference 2023 Conference Paper

The Benefits of Mixup for Feature Learning

• Difan Zou
• Yuan Cao 0006
• Yuanzhi Li
• Quanquan Gu

Mixup, a simple data augmentation method that randomly mixes two data points via linear interpolation, has been extensively applied in various deep learning applications to gain better generalization. However, its theoretical explanation remains largely unclear. In this work, we aim to seek a fundamental understanding of the benefits of Mixup. We first show that Mixup using different linear interpolation parameters for features and labels can still achieve similar performance as standard Mixup. This indicates that the intuitive linearity explanation in Zhang et al. , (2018) may not fully explain the success of Mixup. Then, we perform a theoretical study of Mixup from the feature learning perspective. We consider a feature-noise data model and show that Mixup training can effectively learn the rare features (appearing in a small fraction of data) from its mixture with the common features (appearing in a large fraction of data). In contrast, standard training can only learn the common features but fails to learn the rare features, thus suffering from bad generalization performance. Moreover, our theoretical analysis also shows that the benefits of Mixup for feature learning are mostly gained in the early training phase, based on which we propose to apply early stopping in Mixup. Experimental results verify our theoretical findings and demonstrate the effectiveness of the early-stopped Mixup training.

ICLR Conference 2023 Conference Paper

Understanding the Generalization of Adam in Learning Neural Networks with Proper Regularization

• Difan Zou
• Yuan Cao 0006
• Yuanzhi Li
• Quanquan Gu

Adaptive gradient methods such as Adam have gained increasing popularity in deep learning optimization. However, it has been observed in many deep learning applications such as image classification, Adam can converge to a different solution with a worse test error compared to (stochastic) gradient descent, even with a fine-tuned regularization. In this paper, we provide a theoretical explanation for this phenomenon: we show that in the nonconvex setting of learning over-parameterized two-layer convolutional neural networks starting from the same random initialization, for a class of data distributions (inspired from image data), Adam and gradient descent (GD) can converge to different global solutions of the training objective with provably different generalization errors, even with weight decay regularization. In contrast, we show that if the training objective is convex, and the weight decay regularization is employed, any optimization algorithms including Adam and GD will converge to the same solution if the training is successful. This suggests that the generalization gap between Adam and SGD in the presence of weight decay regularization is closely tied to the nonconvex landscape of deep learning optimization, which cannot be covered by the recent neural tangent kernel (NTK) based analysis.

ICLR Conference 2023 Conference Paper

Understanding Train-Validation Split in Meta-Learning with Neural Networks

• Xinzhe Zuo
• Zixiang Chen
• Huaxiu Yao
• Yuan Cao 0006
• Quanquan Gu

The goal of meta-learning is to learn a good prior model from a collection of tasks such that the learned prior is able to adapt quickly to new tasks without accessing many data from the new tasks. A common practice in meta-learning is to perform a train-validation split on each task, where the training set is used for adapting the model parameter to that specific task and the validation set is used for learning a prior model that is shared across all tasks. Despite its success and popularity in multitask learning and few-shot learning, the understanding of the train-validation split is still limited, especially when the neural network models are used. In this paper, we study the benefit of train-validation split for classification problems with neural network models trained by gradient descent. We prove that the train-validation split is necessary to learn a good prior model when the noise in the training sample is large, while the train-train method fails. We validate our theory by conducting experiment on both synthetic and real datasets. To the best of our knowledge, this is the first work towards the theoretical understanding of train-validation split in meta-learning with neural networks.

UAI Conference 2023 Conference Paper

Uniform-PAC Guarantees for Model-Based RL with Bounded Eluder Dimension

• Yue Wu
• Jiafan He
• Quanquan Gu

Recently, there has been remarkable progress in reinforcement learning (RL) with general function approximation. However, all these works only provide regret or sample complexity guarantees. It is still an open question if one can achieve stronger performance guarantees, i. e. , the uniform probably approximate correctness (Uniform-PAC) guarantee that can imply both a sub-linear regret bound and a polynomial sample complexity for any target learning accuracy. We study this problem by proposing algorithms for both nonlinear bandits and model-based episodic RL using the general function class with a bounded eluder dimension. The key idea of the proposed algorithms is to assign each action to different levels according to its width with respect to the confidence set. The achieved Uniform-PAC sample complexity is tight in the sense that it matches the state-of-the-art regret bounds or sample complexity guarantees when reduced to the linear case. To the best of our knowledge, this is the first work for Uniform-PAC guarantees on bandit and RL that goes beyond linear cases.

NeurIPS Conference 2023 Conference Paper

Why Does Sharpness-Aware Minimization Generalize Better Than SGD?

• Zixiang Chen
• Junkai Zhang
• Yiwen Kou
• Xiangning Chen
• Cho-Jui Hsieh
• Quanquan Gu

The challenge of overfitting, in which the model memorizes the training data and fails to generalize to test data, has become increasingly significant in the training of large neural networks. To tackle this challenge, Sharpness-Aware Minimization (SAM) has emerged as a promising training method, which can improve the generalization of neural networks even in the presence of label noise. However, a deep understanding of how SAM works, especially in the setting of nonlinear neural networks and classification tasks, remains largely missing. This paper fills this gap by demonstrating why SAM generalizes better than Stochastic Gradient Descent (SGD) for a certain data model and two-layer convolutional ReLU networks. The loss landscape of our studied problem is nonsmooth, thus current explanations for the success of SAM based on the Hessian information are insufficient. Our result explains the benefits of SAM, particularly its ability to prevent noise learning in the early stages, thereby facilitating more effective learning of features. Experiments on both synthetic and real data corroborate our theory.

NeurIPS Conference 2022 Conference Paper

A Simple and Provably Efficient Algorithm for Asynchronous Federated Contextual Linear Bandits

• Jiafan He
• Tianhao Wang
• Yifei Min
• Quanquan Gu

We study federated contextual linear bandits, where $M$ agents cooperate with each other to solve a global contextual linear bandit problem with the help of a central server. We consider the asynchronous setting, where all agents work independently and the communication between one agent and the server will not trigger other agents' communication. We propose a simple algorithm named FedLinUCB based on the principle of optimism. We prove that the regret of FedLinUCB is bounded by $\widetilde{\mathcal{O}}(d\sqrt{\sum_{m=1}^M T_m})$ and the communication complexity is $\widetilde{O}(dM^2)$, where $d$ is the dimension of the contextual vector and $T_m$ is the total number of interactions with the environment by agent $m$. To the best of our knowledge, this is the first provably efficient algorithm that allows fully asynchronous communication for federated linear bandits, while achieving the same regret guarantee as in the single-agent setting.

NeurIPS Conference 2022 Conference Paper

Active Ranking without Strong Stochastic Transitivity

• Hao Lou
• Tao Jin
• Yue Wu
• Pan Xu
• Quanquan Gu
• Farzad Farnoud

Ranking from noisy comparisons is of great practical interest in machine learning. In this paper, we consider the problem of recovering the exact full ranking for a list of items under ranking models that do *not* assume the Strong Stochastic Transitivity property. We propose a $$\delta$$-correct algorithm, Probe-Rank, that actively learns the ranking of the items from noisy pairwise comparisons. We prove a sample complexity upper bound for Probe-Rank, which only depends on the preference probabilities between items that are adjacent in the true ranking. This improves upon existing sample complexity results that depend on the preference probabilities for all pairs of items. Probe-Rank thus outperforms existing methods over a large collection of instances that do not satisfy Strong Stochastic Transitivity. Thorough numerical experiments in various settings are conducted, demonstrating that Probe-Rank is significantly more sample-efficient than the state-of-the-art active ranking method.

NeurIPS Conference 2022 Conference Paper

Benign Overfitting in Two-layer Convolutional Neural Networks

• Yuan Cao
• Zixiang Chen
• Misha Belkin
• Quanquan Gu

Modern neural networks often have great expressive power and can be trained to overfit the training data, while still achieving a good test performance. This phenomenon is referred to as “benign overfitting”. Recently, there emerges a line of works studying “benign overfitting” from the theoretical perspective. However, they are limited to linear models or kernel/random feature models, and there is still a lack of theoretical understanding about when and how benign overfitting occurs in neural networks. In this paper, we study the benign overfitting phenomenon in training a two-layer convolutional neural network (CNN). We show that when the signal-to-noise ratio satisfies a certain condition, a two-layer CNN trained by gradient descent can achieve arbitrarily small training and test loss. On the other hand, when this condition does not hold, overfitting becomes harmful and the obtained CNN can only achieve a constant level test loss. These together demonstrate a sharp phase transition between benign overfitting and harmful overfitting, driven by the signal-to-noise ratio. To the best of our knowledge, this is the first work that precisely characterizes the conditions under which benign overfitting can occur in training convolutional neural networks.

NeurIPS Conference 2022 Conference Paper

Computationally Efficient Horizon-Free Reinforcement Learning for Linear Mixture MDPs

• Dongruo Zhou
• Quanquan Gu

Recent studies have shown that episodic reinforcement learning (RL) is not more difficult than bandits, even with a long planning horizon and unknown state transitions. However, these results are limited to either tabular Markov decision processes (MDPs) or computationally inefficient algorithms for linear mixture MDPs. In this paper, we propose the first computationally efficient horizon-free algorithm for linear mixture MDPs, which achieves the optimal $\tilde O(d\sqrt{K} +d^2)$ regret up to logarithmic factors. Our algorithm adapts a weighted least square estimator for the unknown transitional dynamic, where the weight is both \emph{variance-aware} and \emph{uncertainty-aware}. When applying our weighted least square estimator to heterogeneous linear bandits, we can obtain an $\tilde O(d\sqrt{\sum_{k=1}^K \sigma_k^2} +d)$ regret in the first $K$ rounds, where $d$ is the dimension of the context and $\sigma_k^2$ is the variance of the reward in the $k$-th round. This also improves upon the best known algorithms in this setting when $\sigma_k^2$'s are known.

ICML Conference 2022 Conference Paper

Dimension-free Complexity Bounds for High-order Nonconvex Finite-sum Optimization

• Dongruo Zhou
• Quanquan Gu

Stochastic high-order methods for finding first-order stationary points in nonconvex finite-sum optimization have witnessed increasing interest in recent years, and various upper and lower bounds of the oracle complexity have been proved. However, under standard regularity assumptions, existing complexity bounds are all dimension-dependent (e. g. , polylogarithmic dependence), which contrasts with the dimension-free complexity bounds for stochastic first-order methods and deterministic high-order methods. In this paper, we show that the polylogarithmic dimension dependence gap is not essential and can be closed. More specifically, we propose stochastic high-order algorithms with novel first-order and high-order derivative estimators, which can achieve dimension-free complexity bounds. With the access to $p$-th order derivatives of the objective function, we prove that our algorithm finds $\epsilon$-stationary points with $O(n^{(2p-1)/(2p)}/\epsilon^{(p+1)/p})$ high-order oracle complexities, where $n$ is the number of individual functions. Our result strictly improves the complexity bounds of existing high-order deterministic methods with respect to the dependence on $n$, and it is dimension-free compared with existing stochastic high-order methods.

AAAI Conference 2022 Conference Paper

Efficient Robust Training via Backward Smoothing

• Jinghui Chen
• Yu Cheng
• Zhe Gan
• Quanquan Gu
• Jingjing Liu

Adversarial training is so far the most effective strategy in defending against adversarial examples. However, it suffers from high computational costs due to the iterative adversarial attacks in each training step. Recent studies show that it is possible to achieve fast Adversarial Training by performing a single-step attack with random initialization. However, such an approach still lags behind state-of-the-art adversarial training algorithms on both stability and model robustness. In this work, we develop a new understanding towards Fast Adversarial Training, by viewing random initialization as performing randomized smoothing for better optimization of the inner maximization problem. Following this new perspective, we also propose a new initialization strategy, backward smoothing, to further improve the stability and model robustness over single-step robust training methods. Experiments on multiple benchmarks demonstrate that our method achieves similar model robustness as the original TRADES method while using much less training time (∼3x improvement with the same training schedule).

ICML Conference 2022 Conference Paper

Last Iterate Risk Bounds of SGD with Decaying Stepsize for Overparameterized Linear Regression

• Jingfeng Wu
• Difan Zou
• Vladimir Braverman
• Quanquan Gu
• Sham M. Kakade

Stochastic gradient descent (SGD) has been shown to generalize well in many deep learning applications. In practice, one often runs SGD with a geometrically decaying stepsize, i. e. , a constant initial stepsize followed by multiple geometric stepsize decay, and uses the last iterate as the output. This kind of SGD is known to be nearly minimax optimal for classical finite-dimensional linear regression problems (Ge et al. , 2019). However, a sharp analysis for the last iterate of SGD in the overparameterized setting is still open. In this paper, we provide a problem-dependent analysis on the last iterate risk bounds of SGD with decaying stepsize, for (overparameterized) linear regression problems. In particular, for last iterate SGD with (tail) geometrically decaying stepsize, we prove nearly matching upper and lower bounds on the excess risk. Moreover, we provide an excess risk lower bound for last iterate SGD with polynomially decaying stepsize and demonstrate the advantage of geometrically decaying stepsize in an instance-wise manner, which complements the minimax rate comparison made in prior work.

ICLR Conference 2022 Conference Paper

Learning Neural Contextual Bandits through Perturbed Rewards

• Yiling Jia
• Weitong Zhang
• Dongruo Zhou
• Quanquan Gu
• Hongning Wang

Thanks to the power of representation learning, neural contextual bandit algorithms demonstrate remarkable performance improvement against their classical counterparts. But because their exploration has to be performed in the entire neural network parameter space to obtain nearly optimal regret, the resulting computational cost is prohibitively high. We propose to perturb the rewards when updating the neural network to eliminate the need of explicit exploration and the corresponding computational overhead. We prove that a $\tilde{O}(\tilde{d}\sqrt{T})$ regret upper bound is still achievable under standard regularity conditions, where $T$ is the number of rounds of interactions and $\tilde{d}$ is the effective dimension of a neural tangent kernel matrix. Extensive comparisons with several benchmark contextual bandit algorithms, including two recent neural contextual bandit models, demonstrate the effectiveness and computational efficiency of our proposed neural bandit algorithm.

ICML Conference 2022 Conference Paper

Learning Stochastic Shortest Path with Linear Function Approximation

• Yifei Min
• Jiafan He
• Tianhao Wang 0002
• Quanquan Gu

We study the stochastic shortest path (SSP) problem in reinforcement learning with linear function approximation, where the transition kernel is represented as a linear mixture of unknown models. We call this class of SSP problems as linear mixture SSPs. We propose a novel algorithm with Hoeffding-type confidence sets for learning the linear mixture SSP, which can attain an $\tilde{\mathcal{O}}(d B_{\star}^{1. 5}\sqrt{K/c_{\min}})$ regret. Here $K$ is the number of episodes, $d$ is the dimension of the feature mapping in the mixture model, $B_{\star}$ bounds the expected cumulative cost of the optimal policy, and $c_{\min}>0$ is the lower bound of the cost function. Our algorithm also applies to the case when $c_{\min} = 0$, and an $\tilde{\mathcal{O}}(K^{2/3})$ regret is guaranteed. To the best of our knowledge, this is the first algorithm with a sublinear regret guarantee for learning linear mixture SSP. Moreover, we design a refined Bernstein-type confidence set and propose an improved algorithm, which provably achieves an $\tilde{\mathcal{O}}(d B_{\star}\sqrt{K/c_{\min}})$ regret. In complement to the regret upper bounds, we also prove a lower bound of $\Omega(dB_{\star} \sqrt{K})$. Hence, our improved algorithm matches the lower bound up to a $1/\sqrt{c_{\min}}$ factor and poly-logarithmic factors, achieving a near-optimal regret guarantee.

NeurIPS Conference 2022 Conference Paper

Learning Two-Player Markov Games: Neural Function Approximation and Correlated Equilibrium

• Chris Junchi Li
• Dongruo Zhou
• Quanquan Gu
• Michael Jordan

We consider learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation, where the action-value function is approximated by a function in a Reproducing Kernel Hilbert Space (RKHS). The key challenge is how to do exploration in the high-dimensional function space. We propose a novel online learning algorithm to find a Nash equilibrium by minimizing the duality gap. At the core of our algorithms are upper and lower confidence bounds that are derived based on the principle of optimism in the face of uncertainty. We prove that our algorithm is able to attain an $O(\sqrt{T})$ regret with polynomial computational complexity, under very mild assumptions on the reward function and the underlying dynamic of the Markov Games. We also propose several extensions of our algorithm, including an algorithm with Bernstein-type bonus that can achieve a tighter regret bound, and another algorithm for model misspecification that can be applied to neural network function approximation.

NeurIPS Conference 2022 Conference Paper

Nearly Optimal Algorithms for Linear Contextual Bandits with Adversarial Corruptions

• Jiafan He
• Dongruo Zhou
• Tong Zhang
• Quanquan Gu

We study the linear contextual bandit problem in the presence of adversarial corruption, where the reward at each round is corrupted by an adversary, and the corruption level (i. e. , the sum of corruption magnitudes over the horizon) is $C\geq 0$. The best-known algorithms in this setting are limited in that they either are computationally inefficient or require a strong assumption on the corruption, or their regret is at least $C$ times worse than the regret without corruption. In this paper, to overcome these limitations, we propose a new algorithm based on the principle of optimism in the face of uncertainty. At the core of our algorithm is a weighted ridge regression where the weight of each chosen action depends on its confidence up to some threshold. We show that for both known $C$ and unknown $C$ cases, our algorithm with proper choice of hyperparameter achieves a regret that nearly matches the lower bounds. Thus, our algorithm is nearly optimal up to logarithmic factors for both cases. Notably, our algorithm achieves the near-optimal regret for both corrupted and uncorrupted cases ($C=0$) simultaneously.

ICLR Conference 2022 Conference Paper

Neural Contextual Bandits with Deep Representation and Shallow Exploration

• Pan Xu 0002
• Zheng Wen
• Handong Zhao
• Quanquan Gu

We study neural contextual bandits, a general class of contextual bandits, where each context-action pair is associated with a raw feature vector, but the specific reward generating function is unknown. We propose a novel learning algorithm that transforms the raw feature vector using the last hidden layer of a deep ReLU neural network (deep representation learning), and uses an upper confidence bound (UCB) approach to explore in the last linear layer (shallow exploration). We prove that under standard assumptions, our proposed algorithm achieves $\tilde{O}(\sqrt{T})$ finite-time regret, where $T$ is the learning time horizon. Compared with existing neural contextual bandit algorithms, our approach is computationally much more efficient since it only needs to explore in the last layer of the deep neural network.

ICLR Conference 2022 Conference Paper

On the Convergence of Certified Robust Training with Interval Bound Propagation

• Yihan Wang
• Zhouxing Shi
• Quanquan Gu
• Cho-Jui Hsieh

Interval Bound Propagation (IBP) is so far the base of state-of-the-art methods for training neural networks with certifiable robustness guarantees when potential adversarial perturbations present, while the convergence of IBP training remains unknown in existing literature. In this paper, we present a theoretical analysis on the convergence of IBP training. With an overparameterized assumption, we analyze the convergence of IBP robust training. We show that when using IBP training to train a randomly initialized two-layer ReLU neural network with logistic loss, gradient descent can linearly converge to zero robust training error with a high probability if we have sufficiently small perturbation radius and large network width.

ICML Conference 2022 Conference Paper

On the Sample Complexity of Learning Infinite-horizon Discounted Linear Kernel MDPs

• Yuanzhou Chen
• Jiafan He
• Quanquan Gu

We study reinforcement learning for infinite-horizon discounted linear kernel MDPs, where the transition probability function is linear in a predefined feature mapping. Existing UCLK \citep{zhou2020provably} algorithm for this setting only has a regret guarantee, which cannot lead to a tight sample complexity bound. In this paper, we extend the uniform-PAC sample complexity from episodic setting to the infinite-horizon discounted setting, and propose a novel algorithm dubbed UPAC-UCLK that achieves an $\Tilde{O}\big(d^2/((1-\gamma)^4\epsilon^2)+1/((1-\gamma)^6\epsilon^2)\big)$ uniform-PAC sample complexity, where $d$ is the dimension of the feature mapping, $\gamma \in(0, 1)$ is the discount factor of the MDP and $\epsilon$ is the accuracy parameter. To the best of our knowledge, this is the first $\tilde{O}(1/\epsilon^2)$ sample complexity bound for learning infinite-horizon discounted MDPs with linear function approximation (without access to the generative model).

NeurIPS Conference 2022 Conference Paper

Risk Bounds of Multi-Pass SGD for Least Squares in the Interpolation Regime

• Difan Zou
• Jingfeng Wu
• Vladimir Braverman
• Quanquan Gu
• Sham Kakade

Stochastic gradient descent (SGD) has achieved great success due to its superior performance in both optimization and generalization. Most of existing generalization analyses are made for single-pass SGD, which is a less practical variant compared to the commonly-used multi-pass SGD. Besides, theoretical analyses for multi-pass SGD often concern a worst-case instance in a class of problems, which may be pessimistic to explain the superior generalization ability for some particular problem instance. The goal of this paper is to provide an instance-dependent excess risk bound of multi-pass SGD for least squares in the interpolation regime, which is expressed as a function of the iteration number, stepsize, and data covariance. We show that the excess risk of SGD can be exactly decomposed into the excess risk of GD and a positive fluctuation error, suggesting that SGD always performs worse, instance-wisely, than GD, in generalization. On the other hand, we show that although SGD needs more iterations than GD to achieve the same level of excess risk, it saves the number of stochastic gradient evaluations, and therefore is preferable in terms of computational time.

NeurIPS Conference 2022 Conference Paper

The Power and Limitation of Pretraining-Finetuning for Linear Regression under Covariate Shift

• Jingfeng Wu
• Difan Zou
• Vladimir Braverman
• Quanquan Gu
• Sham Kakade

We study linear regression under covariate shift, where the marginal distribution over the input covariates differs in the source and the target domains, while the conditional distribution of the output given the input covariates is similar across the two domains. We investigate a transfer learning approach with pretraining on the source data and finetuning based on the target data (both conducted by online SGD) for this problem. We establish sharp instance-dependent excess risk upper and lower bounds for this approach. Our bounds suggest that for a large class of linear regression instances, transfer learning with $O(N^2)$ source data (and scarce or no target data) is as effective as supervised learning with $N$ target data. In addition, we show that finetuning, even with only a small amount of target data, could drastically reduce the amount of source data required by pretraining. Our theory sheds light on the effectiveness and limitation of pretraining as well as the benefits of finetuning for tackling covariate shift problems.

NeurIPS Conference 2022 Conference Paper

Towards Understanding the Mixture-of-Experts Layer in Deep Learning

• Zixiang Chen
• Yihe Deng
• Yue Wu
• Quanquan Gu
• Yuanzhi Li

The Mixture-of-Experts (MoE) layer, a sparsely-activated model controlled by a router, has achieved great success in deep learning. However, the understanding of such architecture remains elusive. In this paper, we formally study how the MoE layer improves the performance of neural network learning and why the mixture model will not collapse into a single model. Our empirical results suggest that the cluster structure of the underlying problem and the non-linearity of the expert are pivotal to the success of MoE. This motivates us to consider a challenging classification problem with intrinsic cluster structures. Theoretically, we proved that this problem is hard to solve by a single expert such as a two-layer convolutional neural network (CNN). Yet with the MoE layer with each expert being a two-layer CNN, the problem can be solved successfully. In particular, our theory shows that the router can learn the cluster-center features, which helps divide the input complex problem into simpler classification sub-problems that individual experts can conquer. To our knowledge, this is the first theoretical result toward formally understanding the mechanism of the MoE layer for deep learning.

ICML Conference 2021 Conference Paper

Agnostic Learning of Halfspaces with Gradient Descent via Soft Margins

• Spencer Frei
• Yuan Cao 0006
• Quanquan Gu

We analyze the properties of gradient descent on convex surrogates for the zero-one loss for the agnostic learning of halfspaces. We show that when a quantity we refer to as the \textit{soft margin} is well-behaved—a condition satisfied by log-concave isotropic distributions among others—minimizers of convex surrogates for the zero-one loss are approximate minimizers for the zero-one loss itself. As standard convex optimization arguments lead to efficient guarantees for minimizing convex surrogates of the zero-one loss, our methods allow for the first positive guarantees for the classification error of halfspaces learned by gradient descent using the binary cross-entropy or hinge loss in the presence of agnostic label noise.

ICML Conference 2021 Conference Paper

Almost Optimal Anytime Algorithm for Batched Multi-Armed Bandits

• Tianyuan Jin
• Jing Tang 0004
• Pan Xu 0002
• Keke Huang
• Xiaokui Xiao
• Quanquan Gu

In batched multi-armed bandit problems, the learner can adaptively pull arms and adjust strategy in batches. In many real applications, not only the regret but also the batch complexity need to be optimized. Existing batched bandit algorithms usually assume that the time horizon T is known in advance. However, many applications involve an unpredictable stopping time. In this paper, we study the anytime batched multi-armed bandit problem. We propose an anytime algorithm that achieves the asymptotically optimal regret for exponential families of reward distributions with $O(\log \log T \ilog^{\alpha} (T))$ \footnote{Notation \ilog^{\alpha} (T) is the result of iteratively applying the logarithm function on T for \alpha times, e. g. , \ilog^{3} (T)=\log\log\log T. } batches, where $\alpha\in O_{T}(1)$. Moreover, we prove that for any constant c>0, no algorithm can achieve the asymptotically optimal regret within c\log\log T batches.

ICLR Conference 2021 Conference Paper

Direction Matters: On the Implicit Bias of Stochastic Gradient Descent with Moderate Learning Rate

• Jingfeng Wu
• Difan Zou
• Vladimir Braverman
• Quanquan Gu

Understanding the algorithmic bias of stochastic gradient descent (SGD) is one of the key challenges in modern machine learning and deep learning theory. Most of the existing works, however, focus on very small or even infinitesimal learning rate regime, and fail to cover practical scenarios where the learning rate is moderate and annealing. In this paper, we make an initial attempt to characterize the particular regularization effect of SGD in the moderate learning rate regime by studying its behavior for optimizing an overparameterized linear regression problem. In this case, SGD and GD are known to converge to the unique minimum-norm solution; however, with the moderate and annealing learning rate, we show that they exhibit different directional bias: SGD converges along the large eigenvalue directions of the data matrix, while GD goes after the small eigenvalue directions. Furthermore, we show that such directional bias does matter when early stopping is adopted, where the SGD output is nearly optimal but the GD output is suboptimal. Finally, our theory explains several folk arts in practice used for SGD hyperparameter tuning, such as (1) linearly scaling the initial learning rate with batch size; and (2) overrunning SGD with high learning rate even when the loss stops decreasing.

NeurIPS Conference 2021 Conference Paper

Do Wider Neural Networks Really Help Adversarial Robustness?

• Boxi Wu
• Jinghui Chen
• Deng Cai
• Xiaofei He
• Quanquan Gu

Adversarial training is a powerful type of defense against adversarial examples. Previous empirical results suggest that adversarial training requires wider networks for better performances. However, it remains elusive how does neural network width affect model robustness. In this paper, we carefully examine the relationship between network width and model robustness. Specifically, we show that the model robustness is closely related to the tradeoff between natural accuracy and perturbation stability, which is controlled by the robust regularization parameter λ. With the same λ, wider networks can achieve better natural accuracy but worse perturbation stability, leading to a potentially worse overall model robustness. To understand the origin of this phenomenon, we further relate the perturbation stability with the network's local Lipschitzness. By leveraging recent results on neural tangent kernels, we theoretically show that wider networks tend to have worse perturbation stability. Our analyses suggest that: 1) the common strategy of first fine-tuning λ on small networks and then directly use it for wide model training could lead to deteriorated model robustness; 2) one needs to properly enlarge λ to unleash the robustness potential of wider models fully. Finally, we propose a new Width Adjusted Regularization (WAR) method that adaptively enlarges λ on wide models and significantly saves the tuning time.

NeurIPS Conference 2021 Conference Paper

Exploring Architectural Ingredients of Adversarially Robust Deep Neural Networks

• Hanxun Huang
• Yisen Wang
• Sarah Erfani
• Quanquan Gu
• James Bailey
• Xingjun Ma

Deep neural networks (DNNs) are known to be vulnerable to adversarial attacks. A range of defense methods have been proposed to train adversarially robust DNNs, among which adversarial training has demonstrated promising results. However, despite preliminary understandings developed for adversarial training, it is still not clear, from the architectural perspective, what configurations can lead to more robust DNNs. In this paper, we address this gap via a comprehensive investigation on the impact of network width and depth on the robustness of adversarially trained DNNs. Specifically, we make the following key observations: 1) more parameters (higher model capacity) does not necessarily help adversarial robustness; 2) reducing capacity at the last stage (the last group of blocks) of the network can actually improve adversarial robustness; and 3) under the same parameter budget, there exists an optimal architectural configuration for adversarial robustness. We also provide a theoretical analysis explaning why such network configuration can help robustness. These architectural insights can help design adversarially robust DNNs.

UAI Conference 2021 Conference Paper

Faster Convergence of Stochastic Gradient Langevin Dynamics for Non-Log-Concave Sampling

• Difan Zou
• Pan Xu 0002
• Quanquan Gu

We provide a new convergence analysis of stochastic gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave. At the core of our approach is a novel conductance analysis of SGLD using an auxiliary time-reversible Markov Chain. Under certain conditions on the target distribution, we prove that $\tilde O(d^4\epsilon^{-2})$ stochastic gradient evaluations suffice to guarantee $\epsilon$-sampling error in terms of the total variation distance, where $d$ is the problem dimension. This improves existing results on the convergence rate of SGLD [Raginsky et al. , 2017, Xu et al. , 2018]. We further show that provided an additional Hessian Lipschitz condition on the log-density function, SGLD is guaranteed to achieve $\epsilon$-sampling error within $\tilde O(d^{15/4}\epsilon^{-3/2})$ stochastic gradient evaluations. Our proof technique provides a new way to study the convergence of Langevin based algorithms, and sheds some light on the design of fast stochastic gradient based sampling algorithms.

ICLR Conference 2021 Conference Paper

How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks?

• Zixiang Chen
• Yuan Cao 0006
• Difan Zou
• Quanquan Gu

A recent line of research on deep learning focuses on the extremely over-parameterized setting, and shows that when the network width is larger than a high degree polynomial of the training sample size $n$ and the inverse of the target error $\epsilon^{-1}$, deep neural networks learned by (stochastic) gradient descent enjoy nice optimization and generalization guarantees. Very recently, it is shown that under certain margin assumptions on the training data, a polylogarithmic width condition suffices for two-layer ReLU networks to converge and generalize (Ji and Telgarsky, 2020). However, whether deep neural networks can be learned with such a mild over-parameterization is still an open question. In this work, we answer this question affirmatively and establish sharper learning guarantees for deep ReLU networks trained by (stochastic) gradient descent. In specific, under certain assumptions made in previous work, our optimization and generalization guarantees hold with network width polylogarithmic in $n$ and $\epsilon^{-1}$. Our results push the study of over-parameterized deep neural networks towards more practical settings.

NeurIPS Conference 2021 Conference Paper

Iterative Teacher-Aware Learning

• Luyao Yuan
• Dongruo Zhou
• Junhong Shen
• Jingdong Gao
• Jeffrey L Chen
• Quanquan Gu
• Ying Nian Wu
• Song-Chun Zhu

In human pedagogy, teachers and students can interact adaptively to maximize communication efficiency. The teacher adjusts her teaching method for different students, and the student, after getting familiar with the teacher’s instruction mechanism, can infer the teacher’s intention to learn faster. Recently, the benefits of integrating this cooperative pedagogy into machine concept learning in discrete spaces have been proved by multiple works. However, how cooperative pedagogy can facilitate machine parameter learning hasn’t been thoroughly studied. In this paper, we propose a gradient optimization based teacher-aware learner who can incorporate teacher’s cooperative intention into the likelihood function and learn provably faster compared with the naive learning algorithms used in previous machine teaching works. We give theoretical proof that the iterative teacher-aware learning (ITAL) process leads to local and global improvements. We then validate our algorithms with extensive experiments on various tasks including regression, classification, and inverse reinforcement learning using synthetic and real data. We also show the advantage of modeling teacher-awareness when agents are learning from human teachers.

YNICL Journal 2021 Journal Article

Locus coeruleus degeneration is associated with disorganized functional topology in Parkinson’s disease

• Cheng Zhou
• Tao Guo
• Xueqin Bai
• Jingjing Wu
• Ting Gao
• Xiaojun Guan
• Xiaocao Liu
• Luyan Gu

ICML Conference 2021 Conference Paper

Logarithmic Regret for Reinforcement Learning with Linear Function Approximation

• Jiafan He
• Dongruo Zhou
• Quanquan Gu

Reinforcement learning (RL) with linear function approximation has received increasing attention recently. However, existing work has focused on obtaining $\sqrt{T}$-type regret bound, where $T$ is the number of interactions with the MDP. In this paper, we show that logarithmic regret is attainable under two recently proposed linear MDP assumptions provided that there exists a positive sub-optimality gap for the optimal action-value function. More specifically, under the linear MDP assumption (Jin et al. , 2020), the LSVI-UCB algorithm can achieve $\tilde{O}(d^{3}H^5/\text{gap}_{\text{min}}\cdot \log(T))$regret; and under the linear mixture MDP assumption (Ayoub et al. , 2020), the UCRL-VTR algorithm can achieve $\tilde{O}(d^{2}H^5/\text{gap}_{\text{min}}\cdot \log^3(T))$ regret, where $d$ is the dimension of feature mapping, $H$ is the length of episode, $\text{gap}_{\text{min}}$ is the minimal sub-optimality gap, and $\tilde O$ hides all logarithmic terms except $\log(T)$. To the best of our knowledge, these are the first logarithmic regret bounds for RL with linear function approximation. We also establish gap-dependent lower bounds for the two linear MDP models.

ICML Conference 2021 Conference Paper

MOTS: Minimax Optimal Thompson Sampling

• Tianyuan Jin
• Pan Xu 0002
• Jieming Shi 0001
• Xiaokui Xiao
• Quanquan Gu

Thompson sampling is one of the most widely used algorithms in many online decision problems due to its simplicity for implementation and superior empirical performance over other state-of-the-art methods. Despite its popularity and empirical success, it has remained an open problem whether Thompson sampling can achieve the minimax optimal regret O(\sqrt{TK}) for K-armed bandit problems, where T is the total time horizon. In this paper we fill this long open gap by proposing a new Thompson sampling algorithm called MOTS that adaptively truncates the sampling result of the chosen arm at each time step. We prove that this simple variant of Thompson sampling achieves the minimax optimal regret bound O(\sqrt{TK}) for finite time horizon T and also the asymptotic optimal regret bound when $T$ grows to infinity as well. This is the first time that the minimax optimality of multi-armed bandit problems has been attained by Thompson sampling type of algorithms.

NeurIPS Conference 2021 Conference Paper

Nearly Minimax Optimal Reinforcement Learning for Discounted MDPs

• Jiafan He
• Dongruo Zhou
• Quanquan Gu

We study the reinforcement learning problem for discounted Markov Decision Processes (MDPs) under the tabular setting. We propose a model-based algorithm named UCBVI-$\gamma$, which is based on the \emph{optimism in the face of uncertainty principle} and the Bernstein-type bonus. We show that UCBVI-$\gamma$ achieves an $\tilde{O}\big({\sqrt{SAT}}/{(1-\gamma)^{1. 5}}\big)$ regret, where $S$ is the number of states, $A$ is the number of actions, $\gamma$ is the discount factor and $T$ is the number of steps. In addition, we construct a class of hard MDPs and show that for any algorithm, the expected regret is at least $\tilde{\Omega}\big({\sqrt{SAT}}/{(1-\gamma)^{1. 5}}\big)$. Our upper bound matches the minimax lower bound up to logarithmic factors, which suggests that UCBVI-$\gamma$ is nearly minimax optimal for discounted MDPs.

ICLR Conference 2021 Conference Paper

Neural Thompson Sampling

• Weitong Zhang
• Dongruo Zhou
• Lihong Li 0001
• Quanquan Gu

Thompson Sampling (TS) is one of the most effective algorithms for solving contextual multi-armed bandit problems. In this paper, we propose a new algorithm, called Neural Thompson Sampling, which adapts deep neural networks for both exploration and exploitation. At the core of our algorithm is a novel posterior distribution of the reward, where its mean is the neural network approximator, and its variance is built upon the neural tangent features of the corresponding neural network. We prove that, provided the underlying reward function is bounded, the proposed algorithm is guaranteed to achieve a cumulative regret of $O(T^{1/2})$, which matches the regret of other contextual bandit algorithms in terms of total round number $T$. Experimental comparisons with other benchmark bandit algorithms on various data sets corroborate our theory.

ICML Conference 2021 Conference Paper

On the Convergence of Hamiltonian Monte Carlo with Stochastic Gradients

• Difan Zou
• Quanquan Gu

Hamiltonian Monte Carlo (HMC), built based on the Hamilton’s equation, has been witnessed great success in sampling from high-dimensional posterior distributions. However, it also suffers from computational inefficiency, especially for large training datasets. One common idea to overcome this computational bottleneck is using stochastic gradients, which only queries a mini-batch of training data in each iteration. However, unlike the extensive studies on the convergence analysis of HMC using full gradients, few works focus on establishing the convergence guarantees of stochastic gradient HMC algorithms. In this paper, we propose a general framework for proving the convergence rate of HMC with stochastic gradient estimators, for sampling from strongly log-concave and log-smooth target distributions. We show that the convergence to the target distribution in $2$-Wasserstein distance can be guaranteed as long as the stochastic gradient estimator is unbiased and its variance is upper bounded along the algorithm trajectory. We further apply the proposed framework to analyze the convergence rates of HMC with four standard stochastic gradient estimators: mini-batch stochastic gradient (SG), stochastic variance reduced gradient (SVRG), stochastic average gradient (SAGA), and control variate gradient (CVG). Theoretical results explain the inefficiency of mini-batch SG, and suggest that SVRG and SAGA perform better in the tasks with high-precision requirements, while CVG performs better for large dataset. Experiment results verify our theoretical findings.

ICML Conference 2021 Conference Paper

Provable Generalization of SGD-trained Neural Networks of Any Width in the Presence of Adversarial Label Noise

• Spencer Frei
• Yuan Cao 0006
• Quanquan Gu

We consider a one-hidden-layer leaky ReLU network of arbitrary width trained by stochastic gradient descent (SGD) following an arbitrary initialization. We prove that SGD produces neural networks that have classification accuracy competitive with that of the best halfspace over the distribution for a broad class of distributions that includes log-concave isotropic and hard margin distributions. Equivalently, such networks can generalize when the data distribution is linearly separable but corrupted with adversarial label noise, despite the capacity to overfit. To the best of our knowledge, this is the first work to show that overparameterized neural networks trained by SGD can generalize when the data is corrupted with adversarial label noise.

ICML Conference 2021 Conference Paper

Provable Robustness of Adversarial Training for Learning Halfspaces with Noise

• Difan Zou
• Spencer Frei
• Quanquan Gu

We analyze the properties of adversarial training for learning adversarially robust halfspaces in the presence of agnostic label noise. Denoting $\mathsf{OPT}_{p, r}$ as the best classification error achieved by a halfspace that is robust to perturbations of $\ell^{p}$ balls of radius $r$, we show that adversarial training on the standard binary cross-entropy loss yields adversarially robust halfspaces up to classification error $\tilde O(\sqrt{\mathsf{OPT}_{2, r}})$ for $p=2$, and $\tilde O(d^{1/4} \sqrt{\mathsf{OPT}_{\infty, r}})$ when $p=\infty$. Our results hold for distributions satisfying anti-concentration properties enjoyed by log-concave isotropic distributions among others. We additionally show that if one instead uses a non-convex sigmoidal loss, adversarial training yields halfspaces with an improved robust classification error of $O(\mathsf{OPT}_{2, r})$ for $p=2$, and $O(d^{1/4} \mathsf{OPT}_{\infty, r})$ when $p=\infty$. To the best of our knowledge, this is the first work showing that adversarial training provably yields robust classifiers in the presence of noise.

ICML Conference 2021 Conference Paper

Provably Efficient Reinforcement Learning for Discounted MDPs with Feature Mapping

• Dongruo Zhou
• Jiafan He
• Quanquan Gu

Modern tasks in reinforcement learning have large state and action spaces. To deal with them efficiently, one often uses predefined feature mapping to represent states and actions in a low dimensional space. In this paper, we study reinforcement learning for discounted Markov Decision Processes (MDPs), where the transition kernel can be parameterized as a linear function of certain feature mapping. We propose a novel algorithm which makes use of the feature mapping and obtains a $\tilde O(d\sqrt{T}/(1-\gamma)^2)$ regret, where $d$ is the dimension of the feature space, $T$ is the time horizon and $\gamma$ is the discount factor of the MDP. To the best of our knowledge, this is the first polynomial regret bound without accessing a generative model or making strong assumptions such as ergodicity of the MDP. By constructing a special class of MDPs, we also show that for any algorithms, the regret is lower bounded by $\Omega(d\sqrt{T}/(1-\gamma)^{1. 5})$. Our upper and lower bound results together suggest that the proposed reinforcement learning algorithm is near-optimal up to a $(1-\gamma)^{-0. 5}$ factor.

NeurIPS Conference 2021 Conference Paper

Provably Efficient Reinforcement Learning with Linear Function Approximation under Adaptivity Constraints

• Tianhao Wang
• Dongruo Zhou
• Quanquan Gu

We study reinforcement learning (RL) with linear function approximation under the adaptivity constraint. We consider two popular limited adaptivity models: the batch learning model and the rare policy switch model, and propose two efficient online RL algorithms for episodic linear Markov decision processes, where the transition probability and the reward function can be represented as a linear function of some known feature mapping. In specific, for the batch learning model, our proposed LSVI-UCB-Batch algorithm achieves an $\tilde O(\sqrt{d^3H^3T} + dHT/B)$ regret, where $d$ is the dimension of the feature mapping, $H$ is the episode length, $T$ is the number of interactions and $B$ is the number of batches. Our result suggests that it suffices to use only $\sqrt{T/dH}$ batches to obtain $\tilde O(\sqrt{d^3H^3T})$ regret. For the rare policy switch model, our proposed LSVI-UCB-RareSwitch algorithm enjoys an $\tilde O(\sqrt{d^3H^3T[1+T/(dH)]^{dH/B}})$ regret, which implies that $dH\log T$ policy switches suffice to obtain the $\tilde O(\sqrt{d^3H^3T})$ regret. Our algorithms achieve the same regret as the LSVI-UCB algorithm \citep{jin2020provably}, yet with a substantially smaller amount of adaptivity. We also establish a lower bound for the batch learning model, which suggests that the dependency on $B$ in our regret bound is tight.

NeurIPS Conference 2021 Conference Paper

Proxy Convexity: A Unified Framework for the Analysis of Neural Networks Trained by Gradient Descent

• Spencer Frei
• Quanquan Gu

Although the optimization objectives for learning neural networks are highly non-convex, gradient-based methods have been wildly successful at learning neural networks in practice. This juxtaposition has led to a number of recent studies on provable guarantees for neural networks trained by gradient descent. Unfortunately, the techniques in these works are often highly specific to the particular setup in each problem, making it difficult to generalize across different settings. To address this drawback in the literature, we propose a unified non-convex optimization framework for the analysis of neural network training. We introduce the notions of proxy convexity and proxy Polyak-Lojasiewicz (PL) inequalities, which are satisfied if the original objective function induces a proxy objective function that is implicitly minimized when using gradient methods. We show that stochastic gradient descent (SGD) on objectives satisfying proxy convexity or the proxy PL inequality leads to efficient guarantees for proxy objective functions. We further show that many existing guarantees for neural networks trained by gradient descent can be unified through proxy convexity and proxy PL inequalities.

NeurIPS Conference 2021 Conference Paper

Pure Exploration in Kernel and Neural Bandits

• Yinglun Zhu
• Dongruo Zhou
• Ruoxi Jiang
• Quanquan Gu
• Rebecca Willett
• Robert Nowak

We study pure exploration in bandits, where the dimension of the feature representation can be much larger than the number of arms. To overcome the curse of dimensionality, we propose to adaptively embed the feature representation of each arm into a lower-dimensional space and carefully deal with the induced model misspecifications. Our approach is conceptually very different from existing works that can either only handle low-dimensional linear bandits or passively deal with model misspecifications. We showcase the application of our approach to two pure exploration settings that were previously under-studied: (1) the reward function belongs to a possibly infinite-dimensional Reproducing Kernel Hilbert Space, and (2) the reward function is nonlinear and can be approximated by neural networks. Our main results provide sample complexity guarantees that only depend on the effective dimension of the feature spaces in the kernel or neural representations. Extensive experiments conducted on both synthetic and real-world datasets demonstrate the efficacy of our methods.

NeurIPS Conference 2021 Conference Paper

Reward-Free Model-Based Reinforcement Learning with Linear Function Approximation

• Weitong Zhang
• Dongruo Zhou
• Quanquan Gu

We study the model-based reward-free reinforcement learning with linear function approximation for episodic Markov decision processes (MDPs). In this setting, the agent works in two phases. In the exploration phase, the agent interacts with the environment and collects samples without the reward. In the planning phase, the agent is given a specific reward function and uses samples collected from the exploration phase to learn a good policy. We propose a new provably efficient algorithm, called UCRL-RFE under the Linear Mixture MDP assumption, where the transition probability kernel of the MDP can be parameterized by a linear function over certain feature mappings defined on the triplet of state, action, and next state. We show that to obtain an $\epsilon$-optimal policy for arbitrary reward function, UCRL-RFE needs to sample at most $\tilde O(H^5d^2\epsilon^{-2})$ episodes during the exploration phase. Here, $H$ is the length of the episode, $d$ is the dimension of the feature mapping. We also propose a variant of UCRL-RFE using Bernstein-type bonus and show that it needs to sample at most $\tilde O(H^4d(H + d)\epsilon^{-2})$ to achieve an $\epsilon$-optimal policy. By constructing a special class of linear Mixture MDPs, we also prove that for any reward-free algorithm, it needs to sample at least $\tilde \Omega(H^2d\epsilon^{-2})$ episodes to obtain an $\epsilon$-optimal policy. Our upper bound matches the lower bound in terms of the dependence on $\epsilon$ and the dependence on $d$ if $H \ge d$.

NeurIPS Conference 2021 Conference Paper

Risk Bounds for Over-parameterized Maximum Margin Classification on Sub-Gaussian Mixtures

• Yuan Cao
• Quanquan Gu
• Mikhail Belkin

Modern machine learning systems such as deep neural networks are often highly over-parameterized so that they can fit the noisy training data exactly, yet they can still achieve small test errors in practice. In this paper, we study this "benign overfitting" phenomenon of the maximum margin classifier for linear classification problems. Specifically, we consider data generated from sub-Gaussian mixtures, and provide a tight risk bound for the maximum margin linear classifier in the over-parameterized setting. Our results precisely characterize the condition under which benign overfitting can occur in linear classification problems, and improve on previous work. They also have direct implications for over-parameterized logistic regression.

NeurIPS Conference 2021 Conference Paper

The Benefits of Implicit Regularization from SGD in Least Squares Problems

• Difan Zou
• Jingfeng Wu
• Vladimir Braverman
• Quanquan Gu
• Dean P. Foster
• Sham Kakade

Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice, which has been hypothesized to play an important role in the generalization of modern machine learning approaches. In this work, we seek to understand these issues in the simpler setting of linear regression (including both underparameterized and overparameterized regimes), where our goal is to make sharp instance-based comparisons of the implicit regularization afforded by (unregularized) average SGD with the explicit regularization of ridge regression. For a broad class of least squares problem instances (that are natural in high-dimensional settings), we show: (1) for every problem instance and for every ridge parameter, (unregularized) SGD, when provided with \emph{logarithmically} more samples than that provided to the ridge algorithm, generalizes no worse than the ridge solution (provided SGD uses a tuned constant stepsize); (2) conversely, there exist instances (in this wide problem class) where optimally-tuned ridge regression requires \emph{quadratically} more samples than SGD in order to have the same generalization performance. Taken together, our results show that, up to the logarithmic factors, the generalization performance of SGD is always no worse than that of ridge regression in a wide range of overparameterized problems, and, in fact, could be much better for some problem instances. More generally, our results show how algorithmic regularization has important consequences even in simpler (overparameterized) convex settings.

IJCAI Conference 2021 Conference Paper

Towards Understanding the Spectral Bias of Deep Learning

• Yuan Cao
• Zhiying Fang
• Yue Wu
• Ding-Xuan Zhou
• Quanquan Gu

An intriguing phenomenon observed during training neural networks is the spectral bias, which states that neural networks are biased towards learning less complex functions. The priority of learning functions with low complexity might be at the core of explaining the generalization ability of neural networks, and certain efforts have been made to provide a theoretical explanation for spectral bias. However, there is still no satisfying theoretical result justifying the underlying mechanism of spectral bias. In this paper, we give a comprehensive and rigorous explanation for spectral bias and relate it with the neural tangent kernel function proposed in recent work. We prove that the training process of neural networks can be decomposed along different directions defined by the eigenfunctions of the neural tangent kernel, where each direction has its own convergence rate and the rate is determined by the corresponding eigenvalue. We then provide a case study when the input data is uniformly distributed over the unit sphere, and show that lower degree spherical harmonics are easier to be learned by over-parameterized neural networks. Finally, we provide numerical experiments to demonstrate the correctness of our theory. Our experimental results also show that our theory can tolerate certain model misspecification in terms of the input data distribution.

NeurIPS Conference 2021 Conference Paper

Uniform-PAC Bounds for Reinforcement Learning with Linear Function Approximation

• Jiafan He
• Dongruo Zhou
• Quanquan Gu

We study reinforcement learning (RL) with linear function approximation. Existing algorithms for this problem only have high-probability regret and/or Probably Approximately Correct (PAC) sample complexity guarantees, which cannot guarantee the convergence to the optimal policy. In this paper, in order to overcome the limitation of existing algorithms, we propose a new algorithm called FLUTE, which enjoys uniform-PAC convergence to the optimal policy with high probability. The uniform-PAC guarantee is the strongest possible guarantee for reinforcement learning in the literature, which can directly imply both PAC and high probability regret bounds, making our algorithm superior to all existing algorithms with linear function approximation. At the core of our algorithm is a novel minimax value function estimator and a multi-level partition scheme to select the training samples from historical observations. Both of these techniques are new and of independent interest.

NeurIPS Conference 2021 Conference Paper

Variance-Aware Off-Policy Evaluation with Linear Function Approximation

• Yifei Min
• Tianhao Wang
• Dongruo Zhou
• Quanquan Gu

We study the off-policy evaluation (OPE) problem in reinforcement learning with linear function approximation, which aims to estimate the value function of a target policy based on the offline data collected by a behavior policy. We propose to incorporate the variance information of the value function to improve the sample efficiency of OPE. More specifically, for time-inhomogeneous episodic linear Markov decision processes (MDPs), we propose an algorithm, \texttt{VA-OPE}, which uses the estimated variance of the value function to reweight the Bellman residual in Fitted Q-Iteration. We show that our algorithm achieves a tighter error bound than the best-known result. We also provide a fine-grained characterization of the distribution shift between the behavior policy and the target policy. Extensive numerical experiments corroborate our theory.

ICML Conference 2020 Conference Paper

A Finite-Time Analysis of Q-Learning with Neural Network Function Approximation

• Pan Xu 0002
• Quanquan Gu

Q-learning with neural network function approximation (neural Q-learning for short) is among the most prevalent deep reinforcement learning algorithms. Despite its empirical success, the non-asymptotic convergence rate of neural Q-learning remains virtually unknown. In this paper, we present a finite-time analysis of a neural Q-learning algorithm, where the data are generated from a Markov decision process, and the action-value function is approximated by a deep ReLU neural network. We prove that neural Q-learning finds the optimal policy with an $O(1/\sqrt{T})$ convergence rate if the neural function approximator is sufficiently overparameterized, where $T$ is the number of iterations. To our best knowledge, our result is the first finite-time analysis of neural Q-learning under non-i. i. d. data assumption.

NeurIPS Conference 2020 Conference Paper

A Finite-Time Analysis of Two Time-Scale Actor-Critic Methods

• Yue Frank Wu
• Weitong Zhang
• Pan Xu
• Quanquan Gu

Actor-critic (AC) methods have exhibited great empirical success compared with other reinforcement learning algorithms, where the actor uses the policy gradient to improve the learning policy and the critic uses temporal difference learning to estimate the policy gradient. Under the two time-scale learning rate schedule, the asymptotic convergence of AC has been well studied in the literature. However, the non-asymptotic convergence and finite sample complexity of actor-critic methods are largely open. In this work, we provide a non-asymptotic analysis for two time-scale actor-critic methods under non-i. i. d. setting. We prove that the actor-critic method is guaranteed to find a first-order stationary point (i. e. , $\|\nabla J(\bm{\theta})\|_2^2 \le \epsilon$) of the non-concave performance function $J(\bm{\theta})$, with $\mathcal{\tilde{O}}(\epsilon^{-2. 5})$ sample complexity. To the best of our knowledge, this is the first work providing finite-time analysis and sample complexity bound for two time-scale actor-critic methods.

AAAI Conference 2020 Conference Paper

A Frank-Wolfe Framework for Efficient and Effective Adversarial Attacks

• Jinghui Chen
• Dongruo Zhou
• Jinfeng Yi
• Quanquan Gu

Depending on how much information an adversary can access to, adversarial attacks can be classified as white-box attack and black-box attack. For white-box attack, optimizationbased attack algorithms such as projected gradient descent (PGD) can achieve relatively high attack success rates within moderate iterates. However, they tend to generate adversarial examples near or upon the boundary of the perturbation set, resulting in large distortion. Furthermore, their corresponding black-box attack algorithms also suffer from high query complexities, thereby limiting their practical usefulness. In this paper, we focus on the problem of developing efficient and effective optimization-based adversarial attack algorithms. In particular, we propose a novel adversarial attack framework for both white-box and black-box settings based on a variant of Frank-Wolfe algorithm. We show in theory that the proposed attack algorithms are efficient with an O(1/ √ T) convergence rate. The empirical results of attacking the ImageNet and MNIST datasets also verify the efficiency and effectiveness of the proposed algorithms. More specifically, our proposed algorithms attain the best attack performances in both white-box and black-box attacks among all baselines, and are more time and query efficient than the state-of-the-art.

NeurIPS Conference 2020 Conference Paper

A Generalized Neural Tangent Kernel Analysis for Two-layer Neural Networks

• Zixiang Chen
• Yuan Cao
• Quanquan Gu
• Tong Zhang

A recent breakthrough in deep learning theory shows that the training of over-parameterized deep neural networks can be characterized by a kernel function called \textit{neural tangent kernel} (NTK). However, it is known that this type of results does not perfectly match the practice, as NTK-based analysis requires the network weights to stay very close to their initialization throughout training, and cannot handle regularizers or gradient noises. In this paper, we provide a generalized neural tangent kernel analysis and show that noisy gradient descent with weight decay can still exhibit a ``kernel-like'' behavior. This implies that the training loss converges linearly up to a certain accuracy. We also establish a novel generalization error bound for two-layer neural networks trained by noisy gradient descent with weight decay.

AAAI Conference 2020 Conference Paper

A Knowledge Transfer Framework for Differentially Private Sparse Learning

• Lingxiao Wang
• Quanquan Gu

We study the problem of estimating high dimensional models with underlying sparse structures while preserving the privacy of each training example. We develop a differentially private high-dimensional sparse learning framework using the idea of knowledge transfer. More specifically, we propose to distill the knowledge from a “teacher” estimator trained on a private dataset, by creating a new dataset from auxiliary features, and then train a differentially private “student” estimator using this new dataset. In addition, we establish the linear convergence rate as well as the utility guarantee for our proposed method. For sparse linear regression and sparse logistic regression, our method achieves improved utility guarantees compared with the best known results (Kifer, Smith and Thakurta 2012; Wang and Gu 2019). We further demonstrate the superiority of our framework through both synthetic and real-world data experiments.

NeurIPS Conference 2020 Conference Paper

Agnostic Learning of a Single Neuron with Gradient Descent

• Spencer Frei
• Yuan Cao
• Quanquan Gu

We consider the problem of learning the best-fitting single neuron as measured by the expected square loss $\E_{(x, y)\sim \mathcal{D}}[(\sigma(w^\top x)-y)^2]$ over some unknown joint distribution $\mathcal{D}$ by using gradient descent to minimize the empirical risk induced by a set of i. i. d. samples $S\sim \mathcal{D}^n$. The activation function $\sigma$ is an arbitrary Lipschitz and non-decreasing function, making the optimization problem nonconvex and nonsmooth in general, and covers typical neural network activation functions and inverse link functions in the generalized linear model setting. In the agnostic PAC learning setting, where no assumption on the relationship between the labels $y$ and the input $x$ is made, if the optimal population risk is $\mathsf{OPT}$, we show that gradient descent achieves population risk $O(\mathsf{OPT})+\eps$ in polynomial time and sample complexity when $\sigma$ is strictly increasing. For the ReLU activation, our population risk guarantee is $O(\mathsf{OPT}^{1/2})+\eps$. When labels take the form $y = \sigma(v^\top x) + \xi$ for zero-mean sub-Gaussian noise $\xi$, we show that the population risk guarantees for gradient descent improve to $\mathsf{OPT} + \eps$. Our sample complexity and runtime guarantees are (almost) dimension independent, and when $\sigma$ is strictly increasing, require no distributional assumptions beyond boundedness. For ReLU, we show the same results under a nondegeneracy assumption for the marginal distribution of the input.

IJCAI Conference 2020 Conference Paper

Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks

• Jinghui Chen
• Dongruo Zhou
• Yiqi Tang
• Ziyan Yang
• Yuan Cao
• Quanquan Gu

Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD) with momentum in training deep neural networks. This leaves how to close the generalization gap of adaptive gradient methods an open problem. In this work, we show that adaptive gradient methods such as Adam, Amsgrad, are sometimes "over adapted". We design a new algorithm, called Partially adaptive momentum estimation method, which unifies the Adam/Amsgrad with SGD by introducing a partial adaptive parameter $p$, to achieve the best from both worlds. We also prove the convergence rate of our proposed algorithm to a stationary point in the stochastic nonconvex optimization setting. Experiments on standard benchmarks show that our proposed algorithm can maintain fast convergence rate as Adam/Amsgrad while generalizing as well as SGD in training deep neural networks. These results would suggest practitioners pick up adaptive gradient methods once again for faster training of deep neural networks.

YNICL Journal 2020 Journal Article

Fixel-based analysis reveals fiber-specific alterations during the progression of Parkinson’s disease

• Yanxuan Li
• Tao Guo
• Xiaojun Guan
• Ting Gao
• Wenshuang Sheng
• Cheng Zhou
• Jingjing Wu
• Min Xuan

Disruption of brain circuits is one of the core mechanisms of Parkinson's disease (PD). Understanding structural connection alterations in PD is important for effective treatment. However, due to methodological limitations, most studies were unable to account for confounding factors such as crossing fibers and were unable to identify damages to specific fiber tracts. In the present study, we aimed to demonstrate tract-specific white matter structural changes in PD patients and their relationship with clinical symptoms. Ninety-eight PD patients, divided into early (ES) and middle stage (MS) groups, and 76 healthy controls (HCs) underwent brain magnetic resonance imaging scans and clinical assessments. Fixel-based analysis was used to investigate fiber tract alterations in PD patients. Compared to HCs, the PD patients showed decreased fiber density (FD) in the corpus callosum (CC), increased FD in the cortical spinal tract (CST), and increased fiber-bundle cross-section (FC, log-transformed: log-FC) in the superior cerebellar peduncle (SCP). Analysis of variance (ANOVA) revealed significant differences in FD in the CST and log-FC in the SCP among the three groups. Post-hoc analysis revealed that the mean FD values of the CST were higher in ES and MS patient groups compared to HCs, and the mean log-FC values of the SCP were higher in ES and MS patient groups compared to HCs. Additionally, the FD values of the CC in PD patients were negatively correlated with the Unified Parkinson's Disease Rating Scale part-III (UPDRS-III) scores (r = -0.257, p = 0.032), Hamilton Depression Rating Scale 17 Items (HAMD-17) scores (r = -0.230, p = 0.033), and Hamilton Anxiety Scale (HAMA) scores (r = -0.248, p = 0.032). Moreover, log-FC values of the SCP (r = 0.274, p = 0.028) and FD values of the CST (r = 0.384, p < 0.001) were positively correlated with the UPDRS-III scores. We concluded that PD patients had both decreased and increased white matter integrity within specific fiber bundles. Additionally, these white matter alterations were different across disease stages, suggesting the occurrence of complex pathological and compensatory changes during the development of PD.

AAAI Conference 2020 Conference Paper

Generalization Error Bounds of Gradient Descent for Learning Over-Parameterized Deep ReLU Networks

• Yuan Cao
• Quanquan Gu

Empirical studies show that gradient-based methods can learn deep neural networks (DNNs) with very good generalization performance in the over-parameterization regime, where DNNs can easily fit a random labeling of the training data. Very recently, a line of work explains in theory that with overparameterization and proper random initialization, gradientbased methods can find the global minima of the training loss for DNNs. However, existing generalization error bounds are unable to explain the good generalization performance of over-parameterized DNNs. The major limitation of most existing generalization bounds is that they are based on uniform convergence and are independent of the training algorithm. In this work, we derive an algorithm-dependent generalization error bound for deep ReLU networks, and show that under certain assumptions on the data distribution, gradient descent (GD) with proper random initialization is able to train a sufficiently over-parameterized DNN to achieve arbitrarily small generalization error. Our work sheds light on explaining the good generalization performance of over-parameterized deep neural networks.

ICLR Conference 2020 Conference Paper

Improving Adversarial Robustness Requires Revisiting Misclassified Examples

• Yisen Wang 0001
• Difan Zou
• Jinfeng Yi
• James Bailey 0001
• Xingjun Ma
• Quanquan Gu

Deep neural networks (DNNs) are vulnerable to adversarial examples crafted by imperceptible perturbations. A range of defense techniques have been proposed to improve DNN robustness to adversarial examples, among which adversarial training has been demonstrated to be the most effective. Adversarial training is often formulated as a min-max optimization problem, with the inner maximization for generating adversarial examples. However, there exists a simple, yet easily overlooked fact that adversarial examples are only defined on correctly classified (natural) examples, but inevitably, some (natural) examples will be misclassified during training. In this paper, we investigate the distinctive influence of misclassified and correctly classified examples on the final robustness of adversarial training. Specifically, we find that misclassified examples indeed have a significant impact on the final robustness. More surprisingly, we find that different maximization techniques on misclassified examples may have a negligible influence on the final robustness, while different minimization techniques are crucial. Motivated by the above discovery, we propose a new defense algorithm called {\em Misclassification Aware adveRsarial Training} (MART), which explicitly differentiates the misclassified and correctly classified examples during the training. We also propose a semi-supervised extension of MART, which can leverage the unlabeled data to further improve the robustness. Experimental results show that MART and its variant could significantly improve the state-of-the-art adversarial robustness.

ICLR Conference 2020 Conference Paper

Improving Neural Language Generation with Spectrum Control

• Lingxiao Wang 0001
• Jing Huang 0019
• Kevin Huang 0002
• Ziniu Hu
• Guangtao Wang
• Quanquan Gu

Recent Transformer-based models such as Transformer-XL and BERT have achieved huge success on various natural language processing tasks. However, contextualized embeddings at the output layer of these powerful models tend to degenerate and occupy an anisotropic cone in the vector space, which is called the representation degeneration problem. In this paper, we propose a novel spectrum control approach to address this degeneration problem. The core idea of our method is to directly guide the spectra training of the output embedding matrix with a slow-decaying singular value prior distribution through a reparameterization framework. We show that our proposed method encourages isotropy of the learned word representations while maintains the modeling power of these contextual neural models. We further provide a theoretical analysis and insight on the benefit of modeling singular value distribution. We demonstrate that our spectrum control method outperforms the state-of-the-art Transformer-XL modeling for language model, and various Transformer-based models for machine translation, on common benchmark datasets for these tasks.

YNICL Journal 2020 Journal Article

Increased thalamic volume and decreased thalamo-precuneus functional connectivity are associated with smoking relapse

• Chao Wang
• Shuyue Wang
• Zhujing Shen
• Wei Qian
• Yeerfan Jiaerken
• Xiao Luo
• Kaicheng Li
• Qingze Zeng

The thalamus, with the highest density of nicotinic acetylcholine receptor (nAChR) in the brain, plays a central role in thalamo-cortical circuits that are implicated in nicotine addiction. However, little is known about whether the thalamo-cortical circuits are potentially predictive of smoking relapse. In the current study, a total of 125 participants (84 treatment-seeking male smokers and 41 age-matched male nonsmokers) were recruited. Structural and functional magnetic resonance images (MRI) were acquired from all participants. After a 12-week smoking cessation treatment with varenicline, the smokers were then divided into relapsers (n = 54) and nonrelapsers (n = 30). Then, we compared thalamic volume and seed-based thalamo-cortical resting state functional connectivity (rsFC) prior to the cessation treatment among relapsers, nonrelapsers and nonsmokers to investigate the associations between thalamic structure/function and smoking relapse. Increased thalamic volume was detected in smokers relative to nonsmokers, and in relapsers relative to nonrelapsers, especially on the left side. Moreover, decreased left thalamo-precuneus rsFC was detected in relapsers relative to nonrelapsers. Additionally, a logistic regression analysis showed that the thalamic volume and thalamo-precuneus rsFC predicted smoking relapse with an accuracy of 75.7%. These novel findings indicate that increased thalamic volume and decreased thalamo-precuneus rsFC are associated with smoking relapse, and these thalamic measures may be used to predict treatment efficacy of nicotine addiction and serve as a potential biomarker for personalized medicine.

ICML Conference 2020 Conference Paper

Neural Contextual Bandits with UCB-based Exploration

• Dongruo Zhou
• Lihong Li 0001
• Quanquan Gu

We study the stochastic contextual bandit problem, where the reward is generated from an unknown function with additive noise. No assumption is made about the reward function other than boundedness. We propose a new algorithm, NeuralUCB, which leverages the representation power of deep neural networks and uses a neural network-based random feature mapping to construct an upper confidence bound (UCB) of reward for efficient exploration. We prove that, under standard assumptions, NeuralUCB achieves $\tilde O(\sqrt{T})$ regret, where $T$ is the number of rounds. To the best of our knowledge, it is the first neural network-based contextual bandit algorithm with a near-optimal regret guarantee. We also show the algorithm is empirically competitive against representative baselines in a number of benchmarks.

ICLR Conference 2020 Conference Paper

On the Global Convergence of Training Deep Linear ResNets

• Difan Zou
• Philip M. Long
• Quanquan Gu

We study the convergence of gradient descent (GD) and stochastic gradient descent (SGD) for training $L$-hidden-layer linear residual networks (ResNets). We prove that for training deep residual networks with certain linear transformations at input and output layers, which are fixed throughout training, both GD and SGD with zero initialization on all hidden weights can converge to the global minimum of the training loss. Moreover, when specializing to appropriate Gaussian random linear transformations, GD and SGD provably optimize wide enough deep linear ResNets. Compared with the global convergence result of GD for training standard deep linear networks \citep{du2019width}, our condition on the neural network width is sharper by a factor of $O(\kappa L)$, where $\kappa$ denotes the condition number of the covariance matrix of the training data. We further propose a modified identity input and output transformations, and show that a $(d+k)$-wide neural network is sufficient to guarantee the global convergence of GD/SGD, where $d,k$ are the input and output dimensions respectively.

ICML Conference 2020 Conference Paper

Optimization Theory for ReLU Neural Networks Trained with Normalization Layers

• Yonatan Dukler
• Quanquan Gu
• Guido Montúfar

The current paradigm of deep neural networks has been successful in part due to the use of normalization layers. Normalization layers like Batch Normalization, Layer Normalization and Weight Normalization are ubiquitous in practice as they improve the generalization performance and training speed of neural networks significantly. Nonetheless, the vast majority of current deep learning theory and non-convex optimization literature focuses on the un-normalized setting. We bridge this gap by providing the first global convergence result for 2 layer non-linear neural networks with ReLU activations trained with a normalization layer, namely Weight Normalization. The analysis shows how the introduction of normalization layers changes the optimization landscape and in some settings enables faster convergence as compared with un-normalized neural networks.

AAAI Conference 2020 Conference Paper

Rank Aggregation via Heterogeneous Thurstone Preference Models

• Tao Jin
• Pan Xu
• Quanquan Gu
• Farzad Farnoud

We propose the Heterogeneous Thurstone Model (HTM) for aggregating ranked data, which can take the accuracy levels of different users into account. By allowing different noise distributions, the proposed HTM model maintains the generality of Thurstone’s original framework, and as such, also extends the Bradley-Terry-Luce (BTL) model for pairwise comparisons to heterogeneous populations of users. Under this framework, we also propose a rank aggregation algorithm based on alternating gradient descent to estimate the underlying item scores and accuracy levels of different users simultaneously from noisy pairwise comparisons. We theoretically prove that the proposed algorithm converges linearly up to a statistical error which matches that of the state-of-the-art method for the single-user BTL model. We evaluate the proposed HTM model and algorithm on both synthetic and real data, demonstrating that it outperforms existing methods.

ICLR Conference 2020 Conference Paper

Sample Efficient Policy Gradient Methods with Recursive Variance Reduction

• Pan Xu 0002
• Felicia Gao
• Quanquan Gu

Improving the sample efficiency in reinforcement learning has been a long-standing research problem. In this work, we aim to reduce the sample complexity of existing policy gradient methods. We propose a novel policy gradient algorithm called SRVR-PG, which only requires $O(1/\epsilon^{3/2})$\footnote{$O(\cdot)$ notation hides constant factors.} episodes to find an $\epsilon$-approximate stationary point of the nonconcave performance function $J(\boldsymbol{\theta})$ (i.e., $\boldsymbol{\theta}$ such that $\|\nabla J(\boldsymbol{\theta})\|_2^2\leq\epsilon$). This sample complexity improves the existing result $O(1/\epsilon^{5/3})$ for stochastic variance reduced policy gradient algorithms by a factor of $O(1/\epsilon^{1/6})$. In addition, we also propose a variant of SRVR-PG with parameter exploration, which explores the initial policy parameter from a prior probability distribution. We conduct numerical experiments on classic control problems in reinforcement learning to validate the performance of our proposed algorithms.

JMLR Journal 2020 Journal Article

Stochastic Nested Variance Reduction for Nonconvex Optimization

• Dongruo Zhou
• Pan Xu
• Quanquan Gu

We study nonconvex optimization problems, where the objective function is either an average of $n$ nonconvex functions or the expectation of some stochastic function. We propose a new stochastic gradient descent algorithm based on nested variance reduction, namely, Stochastic Nested Variance-Reduced Gradient descent ($\text{SNVRG}$). Compared with conventional stochastic variance reduced gradient ($\text{SVRG}$) algorithm that uses two reference points to construct a semi-stochastic gradient with diminishing variance in each iteration, our algorithm uses $K+1$ nested reference points to build a semi-stochastic gradient to further reduce its variance in each iteration. For smooth nonconvex functions, $\text{SNVRG}$ converges to an $\epsilon$-approximate first-order stationary point within $\tilde O(n\land\epsilon^{-2}+\epsilon^{-3}\land n^{1/2}\epsilon^{-2})$ number of stochastic gradient evaluations. This improves the best known gradient complexity of $\text{SVRG}$ $O(n+n^{2/3}\epsilon^{-2})$ and that of $\text{SCSG}$ $O(n\land \epsilon^{-2}+\epsilon^{-10/3}\land n^{2/3}\epsilon^{-2})$. For gradient dominated functions, $\text{SNVRG}$ also achieves better gradient complexity than the state-of-the-art algorithms. Based on $\text{SNVRG}$, we further propose two algorithms that can find local minima faster than state-of-the-art algorithms in both finite-sum and general stochastic (online) nonconvex optimization. In particular, for finite-sum optimization problems, the proposed $\text{SNVRG}+\text{Neon2}^{\text{finite}}$ algorithm achieves $\tilde{O}(n^{1/2}\epsilon^{-2}+n\epsilon_H^{-3}+n^{3/4}\epsilon_H^{-7/2})$ gradient complexity to converge to an $(\epsilon, \epsilon_H)$-second-order stationary point, which outperforms $\text{SVRG}+\text{Neon2}^{\text{finite}}$ (Allen-Zhu and Li, 2018), the best existing algorithm, in a wide regime. For general stochastic optimization problems, the proposed $\text{SNVRG}+\text{Neon2}^{\text{online}}$ achieves $\tilde{O}(\epsilon^{-3}+\epsilon_H^{-5}+\epsilon^{-2}\epsilon_H^{-3})$ gradient complexity, which is better than both $\text{SVRG}+\text{Neon2}^{\text{online}}$ (Allen-Zhu and Li, 2018) and $\text{Natasha2}$ (Allen-Zhu, 2018a) in certain regimes. Thorough experimental results on different nonconvex optimization problems back up our theory. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

NeurIPS Conference 2019 Conference Paper

Algorithm-Dependent Generalization Bounds for Overparameterized Deep Residual Networks

• Spencer Frei
• Yuan Cao
• Quanquan Gu

The skip-connections used in residual networks have become a standard architecture choice in deep learning due to the increased generalization and stability of networks with this architecture, although there have been limited theoretical guarantees for this improved performance. In this work, we analyze overparameterized deep residual networks trained by gradient descent following random initialization, and demonstrate that (i) the class of networks learned by gradient descent constitutes a small subset of the entire neural network function class, and (ii) this subclass of networks is sufficiently large to guarantee small training error. By showing (i) we are able to demonstrate that deep residual networks trained with gradient descent have a small generalization gap between training and test error, and together with (ii) this guarantees that the test error will be small. Our optimization and generalization guarantees require overparameterization that is only logarithmic in the depth of the network, which helps explain why residual networks are preferable to fully connected ones.

NeurIPS Conference 2019 Conference Paper

An Improved Analysis of Training Over-parameterized Deep Neural Networks

• Difan Zou
• Quanquan Gu

A recent line of research has shown that gradient-based algorithms with random initialization can converge to the global minima of the training loss for over-parameterized (i. e. , sufficiently wide) deep neural networks. However, the condition on the width of the neural network to ensure the global convergence is very stringent, which is often a high-degree polynomial in the training sample size $n$ (e. g. , $O(n^{24})$). In this paper, we provide an improved analysis of the global convergence of (stochastic) gradient descent for training deep neural networks, which only requires a milder over-parameterization condition than previous work in terms of the training sample size and other problem-dependent parameters. The main technical contributions of our analysis include (a) a tighter gradient lower bound that leads to a faster convergence of the algorithm, and (b) a sharper characterization of the trajectory length of the algorithm. By specializing our result to two-layer (i. e. , one-hidden-layer) neural networks, it also provides a milder over-parameterization condition than the best-known result in prior work.

UAI Conference 2019 Conference Paper

An Improved Convergence Analysis of Stochastic Variance-Reduced Policy Gradient

• Pan Xu 0002
• Felicia Gao
• Quanquan Gu

We revisit the stochastic variance-reduced policy gradient (SVRPG) method proposed by \citet{papini2018stochastic} for reinforcement learning. We provide an improved convergence analysis of SVRPG and show that it can find an $\epsilon$-approximate stationary point of the performance function within $O(1/\epsilon^{5/3})$ trajectories. This sample complexity improves upon the best known result $O(1/\epsilon^2)$ by a factor of $O(1/\epsilon^{1/3})$. At the core of our analysis is (i) a tighter upper bound for the variance of importance sampling weights, where we prove that the variance can be controlled by the parameter distance between different policies; and (ii) a fine-grained analysis of the epoch length and batch size parameters such that we can significantly reduce the number of trajectories required in each iteration of SVRPG. We also empirically demonstrate the effectiveness of our theoretical claims of batch sizes on reinforcement learning benchmark tasks.

IJCAI Conference 2019 Conference Paper

Differentially Private Iterative Gradient Hard Thresholding for Sparse Learning

• Lingxiao Wang
• Quanquan Gu

We consider the differentially private sparse learning problem, where the goal is to estimate the underlying sparse parameter vector of a statistical model in the high-dimensional regime while preserving the privacy of each training example. We propose a generic differentially private iterative gradient hard threshoding algorithm with a linear convergence rate and strong utility guarantee. We demonstrate the superiority of our algorithm through two specific applications: sparse linear regression and sparse logistic regression. Specifically, for sparse linear regression, our algorithm can achieve the best known utility guarantee without any extra support selection procedure used in previous work \cite{kifer2012private}. For sparse logistic regression, our algorithm can obtain the utility guarantee with a logarithmic dependence on the problem dimension. Experiments on both synthetic data and real world datasets verify the effectiveness of our proposed algorithm.

NeurIPS Conference 2019 Conference Paper

Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks

• Yuan Cao
• Quanquan Gu

We study the training and generalization of deep neural networks (DNNs) in the over-parameterized regime, where the network width (i. e. , number of hidden nodes per layer) is much larger than the number of training data points. We show that, the expected $0$-$1$ loss of a wide enough ReLU network trained with stochastic gradient descent (SGD) and random initialization can be bounded by the training loss of a random feature model induced by the network gradient at initialization, which we call a \textit{neural tangent random feature} (NTRF) model. For data distributions that can be classified by NTRF model with sufficiently small error, our result yields a generalization error bound in the order of $\tilde{\mathcal{O}}(n^{-1/2})$ that is independent of the network width. Our result is more general and sharper than many existing generalization error bounds for over-parameterized neural networks. In addition, we establish a strong connection between our generalization error bound and the neural tangent kernel (NTK) proposed in recent work.

NeurIPS Conference 2019 Conference Paper

Layer-Dependent Importance Sampling for Training Deep and Large Graph Convolutional Networks

• Difan Zou
• Ziniu Hu
• Yewen Wang
• Song Jiang
• Yizhou Sun
• Quanquan Gu

Graph convolutional networks (GCNs) have recently received wide attentions, due to their successful applications in different graph tasks and different domains. Training GCNs for a large graph, however, is still a challenge. Original full-batch GCN training requires calculating the representation of all the nodes in the graph per GCN layer, which brings in high computation and memory costs. To alleviate this issue, several sampling-based methods are proposed to train GCNs on a subset of nodes. Among them, the node-wise neighbor-sampling method recursively samples a fixed number of neighbor nodes, and thus its computation cost suffers from exponential growing neighbor size across layers; while the layer-wise importance-sampling method discards the neighbor-dependent constraints, and thus the nodes sampled across layer suffer from sparse connection problem. To deal with the above two problems, we propose a new effective sampling algorithm called LAyer-Dependent ImportancE Sampling (LADIES). Based on the sampled nodes in the upper layer, LADIES selects nodes that are in the neighborhood of these nodes and uses the constructed bipartite graph to compute the importance probability. Then, it samples a fixed number of nodes according to the probability for the whole layer, and recursively conducts such procedure per layer to construct the whole computation graph. We prove theoretically and experimentally, that our proposed sampling algorithm outperforms the previous sampling methods regarding both time and memory. Furthermore, LADIES is shown to have better generalization accuracy than original full-batch GCN, due to its stochastic nature.

ICML Conference 2019 Conference Paper

Lower Bounds for Smooth Nonconvex Finite-Sum Optimization

• Dongruo Zhou
• Quanquan Gu

Smooth finite-sum optimization has been widely studied in both convex and nonconvex settings. However, existing lower bounds for finite-sum optimization are mostly limited to the setting where each component function is (strongly) convex, while the lower bounds for nonconvex finite-sum optimization remain largely unsolved. In this paper, we study the lower bounds for smooth nonconvex finite-sum optimization, where the objective function is the average of $n$ nonconvex component functions. We prove tight lower bounds for the complexity of finding $\epsilon$-suboptimal point and $\epsilon$-approximate stationary point in different settings, for a wide regime of the smallest eigenvalue of the Hessian of the objective function (or each component function). Given our lower bounds, we can show that existing algorithms including {KatyushaX} \citep{allen2018katyushax}, {Natasha} \citep{allen2017natasha} and {StagewiseKatyusha} \citep{yang2018does} have achieved optimal {Incremental First-order Oracle} (IFO) complexity (i. e. , number of IFO calls) up to logarithm factors for nonconvex finite-sum optimization. We also point out potential ways to further improve these complexity results, in terms of making stronger assumptions or by a different convergence analysis.

ICML Conference 2019 Conference Paper

On the Convergence and Robustness of Adversarial Training

• Yisen Wang 0001
• Xingjun Ma
• James Bailey 0001
• Jinfeng Yi
• Bowen Zhou 0001
• Quanquan Gu

Improving the robustness of deep neural networks (DNNs) to adversarial examples is an important yet challenging problem for secure deep learning. Across existing defense techniques, adversarial training with Projected Gradient Decent (PGD) is amongst the most effective. Adversarial training solves a min-max optimization problem, with the inner maximization generating adversarial examples by maximizing the classification loss, and the outer minimization finding model parameters by minimizing the loss on adversarial examples generated from the inner maximization. A criterion that measures how well the inner maximization is solved is therefore crucial for adversarial training. In this paper, we propose such a criterion, namely First-Order Stationary Condition for constrained optimization (FOSC), to quantitatively evaluate the convergence quality of adversarial examples found in the inner maximization. With FOSC, we find that to ensure better robustness, it is essential to use adversarial examples with better convergence quality at the later stages of training. Yet at the early stages, high convergence quality adversarial examples are not necessary and may even lead to poor robustness. Based on these observations, we propose a dynamic training strategy to gradually increase the convergence quality of the generated adversarial examples, which significantly improves the robustness of adversarial training. Our theoretical and empirical results show the effectiveness of the proposed method.

NeurIPS Conference 2019 Conference Paper

Stochastic Gradient Hamiltonian Monte Carlo Methods with Recursive Variance Reduction

• Difan Zou
• Pan Xu
• Quanquan Gu

Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) algorithms have received increasing attention in both theory and practice. In this paper, we propose a Stochastic Recursive Variance-Reduced gradient HMC (SRVR-HMC) algorithm. It makes use of a semi-stochastic gradient estimator that recursively accumulates the gradient information to reduce the variance of the stochastic gradient. We provide a convergence analysis of SRVR-HMC for sampling from a class of non-log-concave distributions and show that SRVR-HMC converges faster than all existing HMC-type algorithms based on underdamped Langevin dynamics. Thorough experiments on synthetic and real-world datasets validate our theory and demonstrate the superiority of SRVR-HMC.

JMLR Journal 2019 Journal Article

Stochastic Variance-Reduced Cubic Regularization Methods

• Dongruo Zhou
• Pan Xu
• Quanquan Gu

We propose a stochastic variance-reduced cubic regularized Newton method (SVRC) for non-convex optimization. At the core of SVRC is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for cubic regularization method. For a nonconvex function with $n$ component functions, we show that our algorithm is guaranteed to converge to an $(\epsilon,\sqrt{\epsilon})$-approximate local minimum within $\tilde{O}(n^{4/5}/\epsilon^{3/2})$\footnote{Here $\tilde{O}$ hides poly-logarithmic factors.} second-order oracle calls, which outperforms the state-of-the-art cubic regularization algorithms including subsampled cubic regularization. To further reduce the sample complexity of Hessian matrix computation in cubic regularization based methods, we also propose a sample efficient stochastic variance-reduced cubic regularization (Lite-SVRC) algorithm for finding the local minimum more efficiently. Lite-SVRC converges to an $(\epsilon,\sqrt{\epsilon})$-approximate local minimum within $\tilde{O}(n+n^{2/3}/\epsilon^{3/2})$ Hessian sample complexity, which is faster than all existing cubic regularization based methods. Numerical experiments with different nonconvex optimization problems conducted on real datasets validate our theoretical results for both SVRC and Lite-SVRC. [abs] [ pdf ][ bib ] &copy JMLR 2019. ( edit, beta )

NeurIPS Conference 2019 Conference Paper

Tight Sample Complexity of Learning One-hidden-layer Convolutional Neural Networks

• Yuan Cao
• Quanquan Gu

We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high probability, the proposed algorithm with random initialization grants a linear convergence to the ground-truth parameters up to statistical precision. Compared with existing work, our result applies to general non-trivial, monotonic and Lipschitz continuous activation functions including ReLU, Leaky ReLU, Sigmod and Softplus etc. Moreover, our sample complexity beats existing results in the dependency of the number of hidden nodes and filter size. In fact, our result matches the information-theoretic lower bound for learning one-hidden-layer CNNs with linear activation functions, suggesting that our sample complexity is tight. Our theoretical analysis is backed up by numerical experiments.

ICML Conference 2018 Conference Paper

A Primal-Dual Analysis of Global Optimality in Nonconvex Low-Rank Matrix Recovery

• Xiao Zhang 0016
• Lingxiao Wang 0001
• Yaodong Yu
• Quanquan Gu

We propose a primal-dual based framework for analyzing the global optimality of nonconvex low-rank matrix recovery. Our analysis are based on the restricted strongly convex and smooth conditions, which can be verified for a broad family of loss functions. In addition, our analytic framework can directly handle the widely-used incoherence constraints through the lens of duality. We illustrate the applicability of the proposed framework to matrix completion and one-bit matrix completion, and prove that all these problems have no spurious local minima. Our results not only improve the sample complexity required for characterizing the global optimality of matrix completion, but also resolve an open problem in Ge et al. (2017) regarding one-bit matrix completion. Numerical experiments show that primal-dual based algorithm can successfully recover the global optimum for various low-rank problems.

ICML Conference 2018 Conference Paper

Continuous and Discrete-time Accelerated Stochastic Mirror Descent for Strongly Convex Functions

• Pan Xu 0002
• Tianhao Wang 0002
• Quanquan Gu

We provide a second-order stochastic differential equation (SDE), which characterizes the continuous-time dynamics of accelerated stochastic mirror descent (ASMD) for strongly convex functions. This SDE plays a central role in designing new discrete-time ASMD algorithms via numerical discretization, and providing neat analyses of their convergence rates based on Lyapunov functions. Our results suggest that the only existing ASMD algorithm, namely, AC-SA proposed in Ghadimi & Lan (2012) is one instance of its kind, and we can actually derive new instances of ASMD with fewer tuning parameters. This sheds light on revisiting accelerated stochastic optimization through the lens of SDEs, which can lead to a better understanding of acceleration in stochastic optimization, as well as new simpler algorithms. Numerical experiments on both synthetic and real data support our theory.

ICML Conference 2018 Conference Paper

Covariate Adjusted Precision Matrix Estimation via Nonconvex Optimization

• Jinghui Chen
• Pan Xu 0002
• Lingxiao Wang 0001
• Jian Ma 0004
• Quanquan Gu

We propose a nonconvex estimator for the covariate adjusted precision matrix estimation problem in the high dimensional regime, under sparsity constraints. To solve this estimator, we propose an alternating gradient descent algorithm with hard thresholding. Compared with existing methods along this line of research, which lack theoretical guarantees in optimization error and/or statistical error, the proposed algorithm not only is computationally much more efficient with a linear rate of convergence, but also attains the optimal statistical rate up to a logarithmic factor. Thorough experiments on both synthetic and real data support our theory.

NeurIPS Conference 2018 Conference Paper

Distributed Learning without Distress: Privacy-Preserving Empirical Risk Minimization

• Bargav Jayaraman
• Lingxiao Wang
• David Evans
• Quanquan Gu

Distributed learning allows a group of independent data owners to collaboratively learn a model over their data sets without exposing their private data. We present a distributed learning approach that combines differential privacy with secure multi-party computation. We explore two popular methods of differential privacy, output perturbation and gradient perturbation, and advance the state-of-the-art for both methods in the distributed learning setting. In our output perturbation method, the parties combine local models within a secure computation and then add the required differential privacy noise before revealing the model. In our gradient perturbation method, the data owners collaboratively train a global model via an iterative learning algorithm. At each iteration, the parties aggregate their local gradients within a secure computation, adding sufficient noise to ensure privacy before the gradient updates are revealed. For both methods, we show that the noise can be reduced in the multi-party setting by adding the noise inside the secure computation after aggregation, asymptotically improving upon the best previous results. Experiments on real world data sets demonstrate that our methods provide substantial utility gains for typical privacy requirements.

ICML Conference 2018 Conference Paper

Fast and Sample Efficient Inductive Matrix Completion via Multi-Phase Procrustes Flow

• Xiao Zhang 0016
• Simon S. Du
• Quanquan Gu

We revisit the inductive matrix completion problem that aims to recover a rank-$r$ matrix with ambient dimension $d$ given $n$ features as the side prior information. The goal is to make use of the known $n$ features to reduce sample and computational complexities. We present and analyze a new gradient-based non-convex optimization algorithm that converges to the true underlying matrix at a linear rate with sample complexity only linearly depending on $n$ and logarithmically depending on $d$. To the best of our knowledge, all previous algorithms either have a quadratic dependency on the number of features in sample complexity or a sub-linear computational convergence rate. In addition, we provide experiments on both synthetic and real world data to demonstrate the effectiveness of our proposed algorithm.

NeurIPS Conference 2018 Conference Paper

Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimization

• Pan Xu
• Jinghui Chen
• Difan Zou
• Quanquan Gu

We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with $n$ component functions. At the core of our analysis is a direct analysis of the ergodicity of the numerical approximations to Langevin dynamics, which leads to faster convergence rates. Specifically, we show that gradient Langevin dynamics (GLD) and stochastic gradient Langevin dynamics (SGLD) converge to the \textit{almost minimizer}\footnote{Following \citet{raginsky2017non}, an almost minimizer is defined to be a point which is within the ball of the global minimizer with radius $O(d\log(\beta+1)/\beta)$, where $d$ is the problem dimension and $\beta$ is the inverse temperature parameter. } within $\tilde O\big(nd/(\lambda\epsilon) \big)$\footnote{$\tilde O(\cdot)$ notation hides polynomials of logarithmic terms and constants. } and $\tilde O\big(d^7/(\lambda^5\epsilon^5) \big)$ stochastic gradient evaluations respectively, where $d$ is the problem dimension, and $\lambda$ is the spectral gap of the Markov chain generated by GLD. Both results improve upon the best known gradient complexity\footnote{Gradient complexity is defined as the total number of stochastic gradient evaluations of an algorithm, which is the number of stochastic gradients calculated per iteration times the total number of iterations. } results \citep{raginsky2017non}. Furthermore, for the first time we prove the global convergence guarantee for variance reduced stochastic gradient Langevin dynamics (VR-SGLD) to the almost minimizer within $\tilde O\big(\sqrt{n}d^5/(\lambda^4\epsilon^{5/2})\big)$ stochastic gradient evaluations, which outperforms the gradient complexities of GLD and SGLD in a wide regime. Our theoretical analyses shed some light on using Langevin dynamics based algorithms for nonconvex optimization with provable guarantees.

NeurIPS Conference 2018 Conference Paper

Stochastic Nested Variance Reduction for Nonconvex Optimization

• Dongruo Zhou
• Pan Xu
• Quanquan Gu

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with conventional stochastic variance reduced gradient (SVRG) algorithm that uses two reference points to construct a semi-stochastic gradient with diminishing variance in each iteration, our algorithm uses $K+1$ nested reference points to build a semi-stochastic gradient to further reduce its variance in each iteration. For smooth nonconvex functions, the proposed algorithm converges to an $\epsilon$-approximate first-order stationary point (i. e. , $\|\nabla F(\mathbf{x})\|_2\leq \epsilon$) within $\tilde O(n\land \epsilon^{-2}+\epsilon^{-3}\land n^{1/2}\epsilon^{-2})$\footnote{$\tilde O(\cdot)$ hides the logarithmic factors, and $a\land b$ means $\min(a, b)$. } number of stochastic gradient evaluations. This improves the best known gradient complexity of SVRG $O(n+n^{2/3}\epsilon^{-2})$ and that of SCSG $O(n\land \epsilon^{-2}+\epsilon^{-10/3}\land n^{2/3}\epsilon^{-2})$. For gradient dominated functions, our algorithm also achieves better gradient complexity than the state-of-the-art algorithms. Thorough experimental results on different nonconvex optimization problems back up our theory.

ICML Conference 2018 Conference Paper

Stochastic Variance-Reduced Cubic Regularized Newton Method

• Dongruo Zhou
• Pan Xu 0002
• Quanquan Gu

We propose a stochastic variance-reduced cubic regularized Newton method (SVRC) for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for cubic regularization method. We show that our algorithm is guaranteed to converge to an $(\epsilon, \sqrt{\epsilon})$-approximate local minimum within $\tilde{O}(n^{4/5}/\epsilon^{3/2})$ second-order oracle calls, which outperforms the state-of-the-art cubic regularization algorithms including subsampled cubic regularization. Our work also sheds light on the application of variance reduction technique to high-order non-convex optimization methods. Thorough experiments on various non-convex optimization problems support our theory.

ICML Conference 2018 Conference Paper

Stochastic Variance-Reduced Hamilton Monte Carlo Methods

• Difan Zou
• Pan Xu 0002
• Quanquan Gu

We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution. At the core of our proposed method is a variance reduction technique inspired by the recent advance in stochastic optimization. We show that, to achieve $\epsilon$ accuracy in 2-Wasserstein distance, our algorithm achieves $\tilde O\big(n+\kappa^{2}d^{1/2}/\epsilon+\kappa^{4/3}d^{1/3}n^{2/3}/\epsilon^{2/3}\big)$ gradient complexity (i. e. , number of component gradient evaluations), which outperforms the state-of-the-art HMC and stochastic gradient HMC methods in a wide regime. We also extend our algorithm for sampling from smooth and general log-concave distributions, and prove the corresponding gradient complexity as well. Experiments on both synthetic and real data demonstrate the superior performance of our algorithm.

UAI Conference 2018 Conference Paper

Subsampled Stochastic Variance-Reduced Gradient Langevin Dynamics

• Difan Zou
• Pan Xu 0002
• Quanquan Gu

Stochastic variance-reduced gradient Langevin dynamics (SVRG-LD) was recently proposed to improve the performance of stochastic gradient Langevin dynamics (SGLD) by reducing the variance of the stochastic gradient. In this paper, we propose a variant of SVRG-LD, namely SVRG-LD+, which replaces the full gradient in each epoch with a subsampled one. We provide a nonasymptotic analysis of the convergence of SVRG-LD+ in 2-Wasserstein distance, and show that SVRG-LD+ enjoys a lower gradient complexity1 than SVRG-LD, when the sample size is large or the target accuracy requirement is moderate. Our analysis directly implies a sharper convergence rate for SVRG-LD, which improves the existing convergence rate by a factor of κ1/6 n1/6, where κ is the condition number of the log-density function and n is the sample size. Experiments on both synthetic and real-world datasets validate our theoretical results.

NeurIPS Conference 2018 Conference Paper

Third-order Smoothness Helps: Faster Stochastic Optimization Algorithms for Finding Local Minima

• Yaodong Yu
• Pan Xu
• Quanquan Gu

We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently. More specifically, the proposed algorithm only needs $\tilde{O}(\epsilon^{-10/3})$ stochastic gradient evaluations to converge to an approximate local minimum $\mathbf{x}$, which satisfies $\|\nabla f(\mathbf{x})\|_2\leq\epsilon$ and $\lambda_{\min}(\nabla^2 f(\mathbf{x}))\geq -\sqrt{\epsilon}$ in unconstrained stochastic optimization, where $\tilde{O}(\cdot)$ hides logarithm polynomial terms and constants. This improves upon the $\tilde{O}(\epsilon^{-7/2})$ gradient complexity achieved by the state-of-the-art stochastic local minima finding algorithms by a factor of $\tilde{O}(\epsilon^{-1/6})$. Experiments on two nonconvex optimization problems demonstrate the effectiveness of our algorithm and corroborate our theory.

ICML Conference 2017 Conference Paper

A Unified Variance Reduction-Based Framework for Nonconvex Low-Rank Matrix Recovery

• Lingxiao Wang 0001
• Xiao Zhang 0016
• Quanquan Gu

We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs projected gradient descent based on a novel semi-stochastic gradient specifically designed for low-rank matrix recovery. Based upon the mild restricted strong convexity and smoothness conditions, we derive a projected notion of the restricted Lipschitz continuous gradient property, and prove that our algorithm enjoys linear convergence rate to the unknown low-rank matrix with an improved computational complexity. Moreover, our algorithm can be employed to both noiseless and noisy observations, where the (near) optimal sample complexity and statistical rate can be attained respectively. We further illustrate the superiority of our generic framework through several specific examples, both theoretically and experimentally.

ICML Conference 2017 Conference Paper

High-Dimensional Variance-Reduced Stochastic Gradient Expectation-Maximization Algorithm

• Rongda Zhu
• Lingxiao Wang 0001
• ChengXiang Zhai
• Quanquan Gu

We propose a generic stochastic expectation-maximization (EM) algorithm for the estimation of high-dimensional latent variable models. At the core of our algorithm is a novel semi-stochastic variance-reduced gradient designed for the $Q$-function in the EM algorithm. Under a mild condition on the initialization, our algorithm is guaranteed to attain a linear convergence rate to the unknown parameter of the latent variable model, and achieve an optimal statistical rate up to a logarithmic factor for parameter estimation. Compared with existing high-dimensional EM algorithms, our algorithm enjoys a better computational complexity and is therefore more efficient. We apply our generic algorithm to two illustrative latent variable models: Gaussian mixture model and mixture of linear regression, and demonstrate the advantages of our algorithm by both theoretical analysis and numerical experiments. We believe that the proposed semi-stochastic gradient is of independent interest for general nonconvex optimization problems with bivariate structures.

ICML Conference 2017 Conference Paper

Robust Gaussian Graphical Model Estimation with Arbitrary Corruption

• Lingxiao Wang 0001
• Quanquan Gu

We study the problem of estimating the high-dimensional Gaussian graphical model where the data are arbitrarily corrupted. We propose a robust estimator for the sparse precision matrix in the high-dimensional regime. At the core of our method is a robust covariance matrix estimator, which is based on truncated inner product. We establish the statistical guarantee of our estimator on both estimation error and model selection consistency. In particular, we show that provided that the number of corrupted samples $n_2$ for each variable satisfies $n_2 \lesssim \sqrt{n}/\sqrt{\log d}$, where $n$ is the sample size and $d$ is the number of variables, the proposed robust precision matrix estimator attains the same statistical rate as the standard estimator for Gaussian graphical models. In addition, we propose a hypothesis testing procedure to assess the uncertainty of our robust estimator. We demonstrate the effectiveness of our method through extensive experiments on both synthetic data and real-world genomic data.

NeurIPS Conference 2017 Conference Paper

Speeding Up Latent Variable Gaussian Graphical Model Estimation via Nonconvex Optimization

• Pan Xu
• Jian Ma
• Quanquan Gu

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank components, we propose a sparsity constrained maximum likelihood estimator based on matrix factorization and an efficient alternating gradient descent algorithm with hard thresholding to solve it. Our algorithm is orders of magnitude faster than the convex relaxation based methods for LVGGM. In addition, we prove that our algorithm is guaranteed to linearly converge to the unknown sparse and low-rank components up to the optimal statistical precision. Experiments on both synthetic and genomic data demonstrate the superiority of our algorithm over the state-of-the-art algorithms and corroborate our theory.

ICML Conference 2017 Conference Paper

Uncertainty Assessment and False Discovery Rate Control in High-Dimensional Granger Causal Inference

• Aditya Chaudhry
• Pan Xu 0002
• Quanquan Gu

Causal inference among high-dimensional time series data proves an important research problem in many fields. While in the classical regime one often establishes causality among time series via a concept known as “Granger causality, ” existing approaches for Granger causal inference in high-dimensional data lack the means to characterize the uncertainty associated with Granger causality estimates (e. g. , p-values and confidence intervals). We make two contributions in this work. First, we introduce a novel asymptotically unbiased Granger causality estimator with corresponding test statistics and confidence intervals to allow, for the first time, uncertainty characterization in high-dimensional Granger causal inference. Second, we introduce a novel method for false discovery rate control that achieves higher power in multiple testing than existing techniques and that can cope with dependent test statistics and dependent observations. We corroborate our theoretical results with experiments on both synthetic data and real-world climatological data.

UAI Conference 2016 Conference Paper

Accelerated Stochastic Block Coordinate Gradient Descent for Sparsity Constrained Nonconvex Optimization

• Jinghui Chen
• Quanquan Gu

of nonzero elements in β, and s is a tuning parameter that controls the sparsity of β. The above problem is common in machine learning and statistics, such as the empirical risk minimization (ERM) and M-estimator, where F (β) is the empirical loss function averaged over the training sample. For example, by choosing the squared loss fi (β) = (hβ, xi i − yi )2 /2, (1. 1) becomes a sparsity constrained linear regression problem (Tropp and Gilbert, 2007). We propose an accelerated stochastic block coordinate descent algorithm for nonconvex optimization under sparsity constraint in the high dimensional regime. The core of our algorithm is leveraging both stochastic partial gradient and full partial gradient restricted to each coordinate block to accelerate the convergence. We prove that the algorithm converges to the unknown true parameter at a linear rate, up to the statistical error of the underlying model. Experiments on both synthetic and real datasets backup our theory.

UAI Conference 2016 Conference Paper

Forward Backward Greedy Algorithms for Multi-Task Learning with Faster Rates

• Lu Tian
• Pan Xu 0002
• Quanquan Gu

A large body of algorithms have been proposed for multi-task learning. However, the effectiveness of many multi-task learning algorithms highly depends on the structural regularization, which incurs bias in the resulting estimators and leads to slower convergence rate. In this paper, we aim at developing a multi-task learning algorithm with faster convergence rate. In particular, we propose a general estimator for multitask learning with row sparsity constraint on the parameter matrix, i. e. , the number of nonzero rows in the parameter matrix being small. The proposed estimator is a nonconvex optimization problem. In order to solve it, we develop a forward backward greedy algorithm with provable guarantee. More specifically, we prove that the output of the greedy algorithm attains a sharper estimation error bound than many state-of-the-art multi-task learning methods. Moreover, our estimator enjoys model selection consistency under a mild condition. Thorough experiments on both synthetic and real-world data demonstrate the effectiveness of our method and back up our theory.

ICML Conference 2016 Conference Paper

On the Statistical Limits of Convex Relaxations

• Zhaoran Wang 0001
• Quanquan Gu
• Han Liu 0001

Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this paper, we study the statistical limits of convex relaxations. Particularly, we consider two problems: Mean estimation for sparse principal submatrix and edge probability estimation for stochastic block model. We exploit the sum-of-squares relaxation hierarchy to sharply characterize the limits of a broad class of convex relaxations. Our result shows statistical optimality needs to be compromised for achieving computational tractability using convex relaxations. Compared with existing results on computational lower bounds for statistical problems, which consider general polynomial-time algorithms and rely on computational hardness hypotheses on problems like planted clique detection, our theory focuses on a broad class of convex relaxations and does not rely on unproven hypotheses.

NeurIPS Conference 2016 Conference Paper

Semiparametric Differential Graph Models

• Pan Xu
• Quanquan Gu

In many cases of network analysis, it is more attractive to study how a network varies under different conditions than an individual static network. We propose a novel graphical model, namely Latent Differential Graph Model, where the networks under two different conditions are represented by two semiparametric elliptical distributions respectively, and the variation of these two networks (i. e. , differential graph) is characterized by the difference between their latent precision matrices. We propose an estimator for the differential graph based on quasi likelihood maximization with nonconvex regularization. We show that our estimator attains a faster statistical rate in parameter estimation than the state-of-the-art methods, and enjoys oracle property under mild conditions. Thorough experiments on both synthetic and real world data support our theory.

ICML Conference 2016 Conference Paper

Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation

• Huan Gui
• Jiawei Han 0001
• Quanquan Gu

We present a unified framework for low-rank matrix estimation with a nonconvex penalty. A proximal gradient homotopy algorithm is proposed to solve the proposed optimization problem. Theoretically, we first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty. Moreover, we rigorously show that under a certain condition on the magnitude of the nonzero singular values, the proposed estimator enjoys oracle property (i. e. , exactly recovers the true rank of the matrix), besides attaining a faster rate. Extensive numerical experiments on both synthetic and real world datasets corroborate our theoretical findings.

NeurIPS Conference 2015 Conference Paper

High Dimensional EM Algorithm: Statistical Optimization and Asymptotic Normality

• Zhaoran Wang
• Quanquan Gu
• Yang Ning
• Han Liu

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estimation. With an appropriate initialization, this algorithm converges at a geometric rate and attains an estimator with the (near-)optimal statistical rate of convergence. (ii) Based on the obtained estimator, we propose a new inferential procedure for testing hypotheses for low dimensional components of high dimensional parameters. For a broad family of statistical models, our framework establishes the first computationally feasible approach for optimal estimation and asymptotic inference in high dimensions.

ICML Conference 2015 Conference Paper

Towards a Lower Sample Complexity for Robust One-bit Compressed Sensing

• Rongda Zhu
• Quanquan Gu

In this paper, we propose a novel algorithm based on nonconvex sparsity-inducing penalty for one-bit compressed sensing. We prove that our algorithm has a sample complexity of O(s/ε^2) for strong signals, and O(s\log d/ε^2) for weak signals, where s is the number of nonzero entries in the signal vector, d is the signal dimension and εis the recovery error. For general signals, the sample complexity of our algorithm lies between O(s/ε^2) and O(s\log d/ε^2). This is a remarkable improvement over the existing best sample complexity O(s\log d/ε^2). Furthermore, we show that our algorithm achieves exact support recovery with high probability for strong signals. Our theory is verified by extensive numerical experiments, which clearly illustrate the superiority of our algorithm for both approximate signal and support recovery in the noisy setting.

UAI Conference 2014 Conference Paper

Batch-Mode Active Learning via Error Bound Minimization

• Quanquan Gu
• Tong Zhang 0001
• Jiawei Han 0001

Active learning has been proven to be quite effective in reducing the human labeling efforts by actively selecting the most informative examples to label. In this paper, we present a batch-mode active learning method based on logistic regression. Our key motivation is an out-of-sample bound on the estimation error of class distribution in logistic regression conditioned on any fixed training sample. It is different from a typical PACstyle passive learning error bound, that relies on the i. i. d. assumption of example-label pairs. In addition, it does not contain the class labels of the training sample. Therefore, it can be immediately used to design an active learning algorithm by minimizing this bound iteratively. We also discuss the connections between the proposed method and some existing active learning approaches. Experiments on benchmark UCI datasets and text datasets demonstrate that the proposed method outperforms the state-of-the-art active learning methods significantly.

NeurIPS Conference 2014 Conference Paper

Robust Tensor Decomposition with Gross Corruption

• Quanquan Gu
• Huan Gui
• Jiawei Han

In this paper, we study the statistical performance of robust tensor decomposition with gross corruption. The observations are noisy realization of the superposition of a low-rank tensor $\mathcal{W}^*$ and an entrywise sparse corruption tensor $\mathcal{V}^*$. Unlike conventional noise with bounded variance in previous convex tensor decomposition analysis, the magnitude of the gross corruption can be arbitrary large. We show that under certain conditions, the true low-rank tensor as well as the sparse corruption tensor can be recovered simultaneously. Our theory yields nonasymptotic Frobenius-norm estimation error bounds for each tensor separately. We show through numerical experiments that our theory can precisely predict the scaling behavior in practice.

NeurIPS Conference 2014 Conference Paper

Sparse PCA with Oracle Property

• Quanquan Gu
• Zhaoran Wang
• Han Liu

In this paper, we study the estimation of the $k$-dimensional sparse principal subspace of covariance matrix $\Sigma$ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i. e. , the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank-$k$, and attains a $\sqrt{s/n}$ statistical rate of convergence with $s$ being the subspace sparsity level and $n$ the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets.

TIST Journal 2012 Journal Article

Latent Community Topic Analysis

• Zhijun Yin
• LiangLiang Cao
• Quanquan Gu
• Jiawei Han

This article studies the problem of latent community topic analysis in text-associated graphs. With the development of social media, a lot of user-generated content is available with user networks. Along with rich information in networks, user graphs can be extended with text information associated with nodes. Topic modeling is a classic problem in text mining and it is interesting to discover the latent topics in text-associated graphs. Different from traditional topic modeling methods considering links, we incorporate community discovery into topic analysis in text-associated graphs to guarantee the topical coherence in the communities so that users in the same community are closely linked to each other and share common latent topics. We handle topic modeling and community discovery in the same framework. In our model we separate the concepts of community and topic, so one community can correspond to multiple topics and multiple communities can share the same topic. We compare different methods and perform extensive experiments on two real datasets. The results confirm our hypothesis that topics could help understand community structure, while community structure could help model topics.

NeurIPS Conference 2012 Conference Paper

Selective Labeling via Error Bound Minimization

• Quanquan Gu
• Tong Zhang
• Jiawei Han
• Chris Ding

In many practical machine learning problems, the acquisition of labeled data is often expensive and/or time consuming. This motivates us to study a problem as follows: given a label budget, how to select data points to label such that the learning performance is optimized. We propose a selective labeling method by analyzing the generalization error of Laplacian regularized Least Squares (LapRLS). In particular, we derive a deterministic generalization error bound for LapRLS trained on subsampled data, and propose to select a subset of data points to label by minimizing this upper bound. Since the minimization is a combinational problem, we relax it into continuous domain and solve it by projected gradient descent. Experiments on benchmark datasets show that the proposed method outperforms the state-of-the-art methods.

UAI Conference 2011 Conference Paper

Generalized Fisher Score for Feature Selection

• Quanquan Gu
• Zhenhui Li
• Jiawei Han 0001

Fisher score is one of the most widely used supervised feature selection methods. However, it selects each feature independently according to their scores under the Fisher criterion, which leads to a suboptimal subset of features. In this paper, we present a generalized Fisher score to jointly select features. It aims at finding an subset of features, which maximize the lower bound of traditional Fisher score. The resulting feature selection problem is a mixed integer programming, which can be reformulated as a quadratically constrained linear programming (QCLP). It is solved by cutting plane algorithm, in each iteration of which a multiple kernel learning problem is solved alternatively by multivariate ridge regression and projected gradient descent. Experiments on benchmark data sets indicate that the proposed method outperforms Fisher score as well as many other state-of-the-art feature selection methods.

IJCAI Conference 2011 Conference Paper

Joint Feature Selection and Subspace Learning

• Quanquan Gu
• Zhenhui Li
• Jiawei Han

Dimensionality reduction is a very important topic in machine learning. It can be generally classified into two categories: feature selection and subspace learning. In the past decades, many methods have been proposed for dimensionality reduction. However, most of these works study feature selection and subspace learning independently. In this paper, we present a framework for joint feature selection and subspace learning. We reformulate the subspace learning problem and use L2, 1-norm on the projection matrix to achieve row-sparsity, which leads to selecting relevant features and learning transformation simultaneously. We discuss two situations of the proposed framework, and present their optimization algorithms. Experiments on benchmark face recognition data sets illustrate that the proposed framework outperforms the state of the art methods overwhelmingly.

AAAI Conference 2011 Conference Paper

Learning a Kernel for Multi-Task Clustering

• Quanquan Gu
• Zhenhui Li
• Jiawei Han

Multi-task learning has received increasing attention in the past decade. Many supervised multi-task learning methods have been proposed, while unsupervised multitask learning is still a rarely studied problem. In this paper, we propose to learn a kernel for multi-task clustering. Our goal is to learn a Reproducing Kernel Hilbert Space, in which the geometric structure of the data in each task is preserved, while the data distributions of any two tasks are as close as possible. This is formulated as a unified kernel learning framework, under which we study two types of kernel learning: nonparametric kernel learning and spectral kernel design. Both types of kernel learning can be solved by linear programming. Experiments on several cross-domain text data sets demonstrate that kernel k-means on the learned kernel can achieve better clustering results than traditional single-task clustering methods. It also outperforms the newly proposed multi-task clustering method.

IJCAI Conference 2011 Conference Paper

On Trivial Solution and Scale Transfer Problems in Graph Regularized NMF

• Quanquan Gu
• Chris Ding
• Jiawei Han

Combining graph regularization with nonnegative matrix (tri-)factorization (NMF) has shown great performance improvement compared with traditional nonnegative matrix (tri-)factorization models due to its ability to utilize the geometric structure of the documents and words. In this paper, we show that these models are not well-defined and suffering from trivial solution and scale transfer problems. In order to solve these common problems, we propose two models for graph regularized nonnegative matrix (tri-)factorization, which can be applied for document clustering and co-clustering respectively. In the proposed models, a Normalized Cut-like constraint is imposed on the cluster assignment matrix to make the optimization problem well-defined. We derive a multiplicative updating algorithm for the proposed models, and prove its convergence. Experiments of clustering and co-clustering on benchmark text data sets demonstratethat the proposed models outperform the originalmodels as well as many other state-of-the-art clustering methods.

IJCAI Conference 2009 Conference Paper

• Quanquan Gu
• Jie Zhou

Nonnegative Matrix Factorization (NMF) has been widely used in machine learning and data mining. It aims to find two nonnegative matrices whose product can well approximate the nonnegative data matrix, which naturally lead to parts-based representation. In this paper, we present a local learning regularized nonnegative matrix factorization (LL- NMF) for clustering. It imposes an additional constraint on NMF that the cluster label of each point can be predicted by the points in its neighborhood. This constraint encodes both the discriminative information and the geometric structure, and is good at clustering data on manifold. An iterative multiplicative updating algorithm is proposed to optimize the objective, and its convergence is guaranteed theoretically. Experiments on many benchmark data sets demonstrate that the proposed method outperforms NMF as well as many state of the art clustering methods.