Arrow Research search

Author name cluster

Songtao Lu

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

40 papers
2 author rows

Possible papers

40

JMLR Journal 2025 Journal Article

Decentralized Bilevel Optimization: A Perspective from Transient Iteration Complexity

  • Boao Kong
  • Shuchen Zhu
  • Songtao Lu
  • Xinmeng Huang
  • Kun Yuan

Stochastic bilevel optimization (SBO) is becoming increasingly essential in machine learning due to its versatility in handling nested structures. To address large-scale SBO, decentralized approaches have emerged as effective paradigms in which nodes communicate with immediate neighbors without a central server, thereby improving communication efficiency and enhancing algorithmic robustness. However, most decentralized SBO algorithms focus solely on asymptotic convergence rates, overlooking transient iteration complexity-the number of iterations required before asymptotic rates dominate, which results in limited understanding of the influence of network topology, data heterogeneity, and the nested bilevel algorithmic structures. To address this issue, this paper introduces D-SOBA, a Decentralized Stochastic One-loop Bilevel Algorithm framework. D-SOBA comprises two variants: D-SOBA-SO, which incorporates second-order Hessian and Jacobian matrices, and D-SOBA-FO, which relies entirely on first-order gradients. We provide a comprehensive non-asymptotic convergence analysis and establish the transient iteration complexity of D-SOBA. This provides the first theoretical understanding of how network topology, data heterogeneity, and nested bilevel structures influence decentralized SBO. Extensive experimental results demonstrate the efficiency and theoretical advantages of D-SOBA. [abs] [ pdf ][ bib ] &copy JMLR 2025. ( edit, beta )

PDF Details

ICLR Conference 2025 Conference Paper

DUET: Decentralized Bilevel Optimization without Lower-Level Strong Convexity

  • Zhen Qin
  • Zhuqing Liu
  • Songtao Lu
  • Yingbin Liang
  • Jia Liu 0002

Decentralized bilevel optimization (DBO) provides a powerful framework for multi-agent systems to solve local bilevel tasks in a decentralized fashion without the need for a central server. However, most existing DBO methods rely on lower-level strong convexity (LLSC) to guarantee unique solutions and a well-defined hypergradient for stationarity measure, hindering their applicability in many practical scenarios not satisfying LLSC. To overcome this limitation, we introduce a new single-loop DBO algorithm called diminishing quadratically-regularized bilevel decentralized optimization (DUET), which eliminates the need for LLSC by introducing a diminishing quadratic regularization to the lower-level (LL) objective. We show that DUET achieves an iteration complexity of $O(1/T^{1-5p-\frac{11}{4}\tau})$ for approximate KKT-stationary point convergence under relaxed assumptions, where $p$ and $\tau $ are control parameters for LL learning rate and averaging, respectively. In addition, our DUET algorithm incorporates gradient tracking to address data heterogeneity, a key challenge in DBO settings. To the best of our knowledge, this is the first work to tackle DBO without LLSC under decentralized settings with data heterogeneity. Numerical experiments validate the theoretical findings and demonstrate the practical effectiveness of our proposed algorithms.

Details

NeurIPS Conference 2025 Conference Paper

Meta-D2AG: Causal Graph Learning with Interventional Dynamic Data

  • Tian Gao
  • Songtao Lu
  • Junkyu Lee
  • Elliot Nelson
  • Debarun Bhattacharjya
  • Yue Yu
  • Miao Liu

Causal discovery in the form of a directed acyclic graph (DAG) for dynamic time series data has been widely studied in various applications. Much of the existing work has focused on observational, offline, and/or stationary settings. In this work, we propose a dynamic DAG discovery algorithm, Meta-D$^2$AG, based on online meta-learning. Meta-D$^2$AG is designed to learn dynamic DAG structures from potentially nonlinear and non-stationary times series datasets, accounting for changes in both parameters and graph structures. Notably, Meta-D$^2$AG explicitly treats data collected at different time points with distribution shifts as distinct domains, which is assumed to occur as a result of external interventions. Moreover, Meta-D$^2$AG contains a new online meta-learning framework to take advantage of the temporal transition among existing domains such that it can quickly adapt to new domains with few measurements. A first-order optimization approach is utilized to efficiently solve the meta-learning framework, and theoretical analysis establishes the identifiability conditions and the convergence of the learning process. We demonstrate the promising performance of our method through better accuracy and sample efficiency on benchmark datasets against state-of-the-art baselines.

PDF Details

NeurIPS Conference 2025 Conference Paper

Objective Soups: Multilingual Multi-Task Modeling for Speech Processing

  • A F M Saif
  • Lisha Chen
  • Xiaodong Cui
  • Songtao Lu
  • Brian Kingsbury
  • Tianyi Chen

The need for training multilingual multi-task speech processing (MSP) models that perform both automatic speech recognition and speech-to-text translation is increasingly evident. However, a significant challenge arises from the conflicts among multiple objectives when using a single model. Multi-objective optimization can address this challenge by facilitating the optimization of multiple conflicting objectives and aligning the gradient updates in a common descent direction. While multi-objective optimization helps avoid conflicting gradient updates, a critical issue is that when there are many objectives, such as in MSP, it is often {\em difficult to find} a common descent direction. This leads to an important question: Is it more effective to separate highly conflicting objectives into different optimization levels or to keep them in a single level? To address this question, this paper investigates three multi-objective MSP formulations, which we refer to as \textbf{objective soup recipes}. These formulations apply multi-objective optimization at different optimization levels to mitigate potential conflicts among all objectives. To keep computation and memory overhead low, we incorporate a lightweight layer‑selection strategy that detects the most conflicting layers and uses only their gradients when computing the conflict‑avoidance direction. We conduct an extensive investigation using the CoVoST v2 dataset for combined multilingual ASR and ST tasks, along with the LibriSpeech and AISHELL-1 datasets for multilingual ASR, to identify highly conflicting objectives and determine the most effective training recipe among the three proposed multi-objective optimization algorithms.

PDF Details

NeurIPS Conference 2025 Conference Paper

Optimality and NP-Hardness of Transformers in Learning Markovian Dynamical Functions

  • Yanna Ding
  • Songtao Lu
  • Yingdong Lu
  • Tomasz Nowicki
  • Jianxi Gao

Transformer architectures can solve unseen tasks based on input-output pairs in a given prompt due to in-context learning (ICL). Existing theoretical studies on ICL have mainly focused on linear regression tasks, often with i. i. d. inputs. To understand how transformers express in-context learning when modeling dynamics-driven functions, we investigate Markovian function learning through a structured ICL setup, where we characterize the loss landscape to reveal underlying optimization behaviors. Specifically, we (1) provide the closed-form expression of the global minimizer (in an enlarged parameter space) for a single-layer linear self-attention (LSA) model; (2) prove that recovering transformer parameters that realize the optimal solution is NP-hard in general, revealing a fundamental limitation of one-layer LSA in representing structured dynamical functions; and (3) supply a novel interpretation of a multilayer LSA as performing preconditioned gradient descent to optimize multiple objectives beyond the square loss. These theoretical results are numerically validated using simplified transformers.

PDF Details

ICLR Conference 2025 Conference Paper

Training Nonlinear Transformers for Chain-of-Thought Inference: A Theoretical Generalization Analysis

  • Hongkang Li
  • Songtao Lu
  • Pin-Yu Chen
  • Xiaodong Cui
  • Meng Wang

Chain-of-Thought (CoT) is an efficient prompting method that enables the reasoning ability of large language models by augmenting the query using multiple examples with multiple intermediate steps. Despite the empirical success, the theoretical understanding of how to train a Transformer to achieve the CoT ability remains less explored. This is primarily due to the technical challenges involved in analyzing the nonconvex optimization on nonlinear attention models. To the best of our knowledge, this work provides the first theoretical study of training Transformers with nonlinear attention to obtain the CoT generalization capability so that the resulting model can inference on unseen tasks when the input is augmented by examples of the new task. We first quantify the required training samples and iterations to train a Transformer model towards CoT ability. We then prove the success of its CoT generalization on unseen tasks with distribution-shifted testing data. Moreover, we theoretically characterize the conditions for an accurate reasoning output by CoT even when the provided reasoning examples contain noises and are not always accurate. In contrast, in-context learning (ICL), which can be viewed as one-step CoT without intermediate steps, may fail to provide an accurate output when CoT does. These theoretical findings are justified through experiments.

Details

ICML Conference 2025 Conference Paper

TSP: A Two-Sided Smoothed Primal-Dual Method for Nonconvex Bilevel Optimization

  • Songtao Lu

Extensive research has shown that a wide range of machine learning problems can be formulated as bilevel optimization, where two levels of learning processes intertwine through distinct sets of optimization variables. However, prevailing approaches often impose stringent assumptions, such as strong convexity of the lower-level loss function or uniqueness of the optimal solution, to enable algorithmic development and convergence analysis. However, these assumptions tend to be overly restrictive in real-world scenarios. In this work, we explore a recently popularized Moreau envelope based reformulation of bilevel optimization problems, accommodating nonconvex objective functions at both levels. We propose a stochastic primal-dual method that incorporates smoothing on both sides, capable of finding Karush-Kuhn-Tucker solutions for this general class of nonconvex bilevel optimization problems. A key feature of our algorithm is its ability to dynamically weigh the lower-level problems, enhancing its performance, particularly in stochastic learning scenarios. Numerical experiments underscore the superiority of our proposed algorithm over existing penalty-based methods in terms of both the convergence rate and the test accuracy.

Details

ICML Conference 2024 Conference Paper

Distributed Bilevel Optimization with Communication Compression

  • Yutong He
  • Jie Hu 0022
  • Xinmeng Huang
  • Songtao Lu
  • Bin Wang
  • Kun Yuan 0001

Stochastic bilevel optimization tackles challenges involving nested optimization structures. Its fast-growing scale nowadays necessitates efficient distributed algorithms. In conventional distributed bilevel methods, each worker must transmit full-dimensional stochastic gradients to the server every iteration, leading to significant communication overhead and thus hindering efficiency and scalability. To resolve this issue, we introduce the first family of distributed bilevel algorithms with communication compression. The primary challenge in algorithmic development is mitigating bias in hypergradient estimation caused by the nested structure. We first propose C-SOBA, a simple yet effective approach with unbiased compression and provable linear speedup convergence. However, it relies on strong assumptions on bounded gradients. To address this limitation, we explore the use of moving average, error feedback, and multi-step compression in bilevel optimization, resulting in a series of advanced algorithms with relaxed assumptions and improved convergence properties. Numerical experiments show that our compressed bilevel algorithms can achieve $10\times$ reduction in communication overhead without severe performance degradation.

Details

ICML Conference 2024 Conference Paper

FADAS: Towards Federated Adaptive Asynchronous Optimization

  • Yujia Wang
  • Shiqiang Wang
  • Songtao Lu
  • Jinghui Chen

Federated learning (FL) has emerged as a widely adopted training paradigm for privacy-preserving machine learning. While the SGD-based FL algorithms have demonstrated considerable success in the past, there is a growing trend towards adopting adaptive federated optimization methods, particularly for the training of large-scale models. However, the conventional synchronous aggregation design poses a significant challenge to the practical deployment of those adaptive federated optimization methods, particularly in the presence of straggler clients. To fill this research gap, this paper introduces federated adaptive asynchronous optimization, named FADAS, a novel method that incorporates asynchronous updates into adaptive federated optimization with provable guarantees. To further enhance the efficiency and resilience of our proposed method in scenarios with significant asynchronous delays, we also extend FADAS with a delay-adaptive learning adjustment strategy. We rigorously establish the convergence rate of the proposed algorithms and empirical results demonstrate the superior performance of FADAS over other asynchronous FL baselines.

Details

ICML Conference 2024 Conference Paper

Federated Neuro-Symbolic Learning

  • Pengwei Xing
  • Songtao Lu
  • Han Yu 0001

Neuro-symbolic learning (NSL) models complex symbolic rule patterns into latent variable distributions by neural networks, which reduces rule search space and generates unseen rules to improve downstream task performance. Centralized NSL learning involves directly acquiring data from downstream tasks, which is not feasible for federated learning (FL). To address this limitation, we shift the focus from such a one-to-one interactive neuro-symbolic paradigm to one-to-many Federated Neuro-Symbolic Learning framework (FedNSL) with latent variables as the FL communication medium. Built on the basis of our novel reformulation of the NSL theory, FedNSL is capable of identifying and addressing rule distribution heterogeneity through a simple and effective Kullback-Leibler (KL) divergence constraint on rule distribution applicable under the FL setting. It further theoretically adjusts variational expectation maximization (V-EM) to reduce the rule search space across domains. This is the first incorporation of distribution-coupled bilevel optimization into FL. Extensive experiments based on both synthetic and real-world data demonstrate significant advantages of FedNSL compared to five state-of-the-art methods. It outperforms the best baseline by 17% and 29% in terms of unbalanced average training accuracy and unseen average testing accuracy, respectively.

Details

ICML Conference 2024 Conference Paper

How Do Nonlinear Transformers Learn and Generalize in In-Context Learning?

  • Hongkang Li
  • Meng Wang 0003
  • Songtao Lu
  • Xiaodong Cui
  • Pin-Yu Chen

Transformer-based large language models have displayed impressive in-context learning capabilities, where a pre-trained model can handle new tasks without fine-tuning by simply augmenting the query with some input-output examples from that task. Despite the empirical success, the mechanics of how to train a Transformer to achieve ICL and the corresponding ICL capacity is mostly elusive due to the technical challenges of analyzing the nonconvex training problems resulting from the nonlinear self-attention and nonlinear activation in Transformers. To the best of our knowledge, this paper provides the first theoretical analysis of the training dynamics of Transformers with nonlinear self-attention and nonlinear MLP, together with the ICL generalization capability of the resulting model. Focusing on a group of binary classification tasks, we train Transformers using data from a subset of these tasks and quantify the impact of various factors on the ICL generalization performance on the remaining unseen tasks with and without data distribution shifts. We also analyze how different components in the learned Transformers contribute to the ICL performance. Furthermore, we provide the first theoretical analysis of how model pruning affects ICL performance and prove that proper magnitude-based pruning can have a minimal impact on ICL while reducing inference costs. These theoretical findings are justified through numerical experiments.

Details

ICLR Conference 2024 Conference Paper

PILOT: An $\mathcal{O}(1/K)$-Convergent Approach for Policy Evaluation with Nonlinear Function Approximation

  • Zhuqing Liu
  • Xin Zhang 0054
  • Jia Liu 0002
  • Zhengyuan Zhu
  • Songtao Lu

Learning an accurate value function for a given policy is a critical step in solving reinforcement learning (RL) problems. So far, however, the convergence speed and sample complexity performances of most existing policy evaluation algorithms remain unsatisfactory, particularly with non-linear function approximation. This challenge motivates us to develop a new path-integrated primal-dual stochastic gradient (PILOT) method, that is able to achieve a fast convergence speed for RL policy evaluation with nonlinear function approximation. To further alleviate the periodic full gradient evaluation requirement, we further propose an enhanced method with an adaptive-batch adjustment called PILOT$^+$. The main advantages of our methods include: i) PILOT allows the use of {\em{constant}} step sizes and achieves the $\mathcal{O}(1/K)$ convergence rate to first-order stationary points of non-convex policy evaluation problems; ii) PILOT is a generic {\em{single}}-timescale algorithm that is also applicable for solving a large class of non-convex strongly-concave minimax optimization problems; iii) By adaptively adjusting the batch size via historical stochastic gradient information, PILOT$^+$ is more sample-efficient empirically without loss of theoretical convergence rate. Our extensive numerical experiments verify our theoretical findings and showcase the high efficiency of the proposed PILOT and PILOT$^+$ algorithms compared with the state-of-the-art methods.

Details

ICML Conference 2024 Conference Paper

SF-DQN: Provable Knowledge Transfer using Successor Feature for Deep Reinforcement Learning

  • Shuai Zhang 0015
  • Heshan Devaka Fernando
  • Miao Liu 0001
  • Keerthiram Murugesan
  • Songtao Lu
  • Pin-Yu Chen
  • Tianyi Chen
  • Meng Wang 0003

This paper studies the transfer reinforcement learning (RL) problem where multiple RL problems have different reward functions but share the same underlying transition dynamics. In this setting, the Q-function of each RL problem (task) can be decomposed into a successor feature (SF) and a reward mapping: the former characterizes the transition dynamics, and the latter characterizes the task-specific reward function. This Q-function decomposition, coupled with a policy improvement operator known as generalized policy improvement (GPI), reduces the sample complexity of finding the optimal Q-function, and thus the SF & GPI framework exhibits promising empirical performance compared to traditional RL methods like Q-learning. However, its theoretical foundations remain largely unestablished, especially when learning the successor features using deep neural networks (SF-DQN). This paper studies the provable knowledge transfer using SFs-DQN in transfer RL problems. We establish the first convergence analysis with provable generalization guarantees for SF-DQN with GPI. The theory reveals that SF-DQN with GPI outperforms conventional RL approaches, such as deep Q-network, in terms of both faster convergence rate and better generalization. Numerical experiments on real and synthetic RL tasks support the superior performance of SF-DQN & GPI, aligning with our theoretical findings.

Details

NeurIPS Conference 2024 Conference Paper

SPARKLE: A Unified Single-Loop Primal-Dual Framework for Decentralized Bilevel Optimization

  • Shuchen Zhu
  • Boao Kong
  • Songtao Lu
  • Xinmeng Huang
  • Kun Yuan

This paper studies decentralized bilevel optimization, in which multiple agents collaborate to solve problems involving nested optimization structures with neighborhood communications. Most existing literature primarily utilizes gradient tracking to mitigate the influence of data heterogeneity, without exploring other well-known heterogeneity-correction techniques such as EXTRA or Exact Diffusion. Additionally, these studies often employ identical decentralized strategies for both upper- and lower-level problems, neglecting to leverage distinct mechanisms across different levels. To address these limitations, this paper proposes SPARKLE, a unified single-loop primal-dual algorithm framework for decentralized bilevel optimization. SPARKLE offers the flexibility to incorporate various heterogeneity-correction strategies into the algorithm. Moreover, SPARKLE allows for different strategies to solve upper- and lower-level problems. We present a unified convergence analysis for SPARKLE, applicable to all its variants, with state-of-the-art convergence rates compared to existing decentralized bilevel algorithms. Our results further reveal that EXTRA and Exact Diffusion are more suitable for decentralized bilevel optimization, and using mixed strategies in bilevel algorithms brings more benefits than relying solely on gradient tracking.

PDF Details DOI

NeurIPS Conference 2023 Conference Paper

An Alternating Optimization Method for Bilevel Problems under the Polyak-Łojasiewicz Condition

  • Quan Xiao
  • Songtao Lu
  • Tianyi Chen

Bilevel optimization has recently regained interest owing to its applications in emerging machine learning fields such as hyperparameter optimization, meta-learning, and reinforcement learning. Recent results have shown that simple alternating (implicit) gradient-based algorithms can match the convergence rate of single-level gradient descent (GD) when addressing bilevel problems with a strongly convex lower-level objective. However, it remains unclear whether this result can be generalized to bilevel problems beyond this basic setting. In this paper, we first introduce a stationary metric for the considered bilevel problems, which generalizes the existing metric, for a nonconvex lower-level objective that satisfies the Polyak-Łojasiewicz (PL) condition. We then propose a Generalized ALternating mEthod for bilevel opTimization (GALET) tailored to BLO with convex PL LL problem and establish that GALET achieves an $\epsilon$-stationary point for the considered problem within $\tilde{\cal O}(\epsilon^{-1})$ iterations, which matches the iteration complexity of GD for single-level smooth nonconvex problems.

PDF Details

ICML Conference 2023 Conference Paper

Bilevel Optimization with Coupled Decision-Dependent Distributions

  • Songtao Lu

Bilevel optimization has gained significant popularity in recent years due to its ability to formulate various machine learning problems. For instance, in meta-learning, the upper-level (UL) problem offers a good initialization for the lower-level (LL) model to facilitate adaptation. However, the decision variables can impact data features and outcomes, leading to the phenomenon known as performativity. In this work, we investigate the inclusion of decision-dependent distributions in bilevel optimization. Specifically, we consider the scenarios where the UL data distribution depends on the LL optimization variable, and the LL data distribution also depends on the UL decision variable. We first establish sufficient conditions for the existence of performatively stable (PS) solutions in this class of bilevel problems. Also, we propose efficient stochastic algorithms to find the PS point with theoretical convergence rate analysis and discuss the theoretical optimality of the obtained solution. Our theoretical analysis is corroborated through a series of numerical experiments, wherein we evaluate the performance of the bilevel performative prediction algorithms alongside non-performative counterparts in the context of meta strategic learning problems.

Details

ICML Conference 2023 Conference Paper

Compressed Decentralized Proximal Stochastic Gradient Method for Nonconvex Composite Problems with Heterogeneous Data

  • Yonggui Yan
  • Jie Chen
  • Pin-Yu Chen
  • Xiaodong Cui
  • Songtao Lu
  • Yangyang Xu

We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save communication cost, we then extend DProxSGT to a compressed method by compressing the communicated information. Both methods need only $\mathcal{O}(1)$ samples per worker for each proximal update, which is important to achieve good generalization performance on training deep neural networks. With a smoothness condition on the expected loss function (but not on each sample function), the proposed methods can achieve an optimal sample complexity result to produce a near-stationary point. Numerical experiments on training neural networks demonstrate the significantly better generalization performance of our methods over large-batch training methods and momentum variance-reduction methods and also, the ability of handling heterogeneous data by the gradient tracking scheme.

Details

ICLR Conference 2023 Conference Paper

Joint Edge-Model Sparse Learning is Provably Efficient for Graph Neural Networks

  • Shuai Zhang 0015
  • Meng Wang 0003
  • Pin-Yu Chen
  • Sijia Liu 0001
  • Songtao Lu
  • Miao Liu 0001

Due to the significant computational challenge of training large-scale graph neural networks (GNNs), various sparse learning techniques have been exploited to reduce memory and storage costs. Examples include graph sparsification that samples a subgraph to reduce the amount of data aggregation and model sparsification that prunes the neural network to reduce the number of trainable weights. Despite the empirical successes in reducing the training cost while maintaining the test accuracy, the theoretical generalization analysis of sparse learning for GNNs remains elusive. To the best of our knowledge, this paper provides the first theoretical characterization of joint edge-model sparse learning from the perspective of sample complexity and convergence rate in achieving zero generalization error. It proves analytically that both sampling important nodes and pruning neurons with lowest-magnitude can reduce the sample complexity and improve convergence without compromising the test accuracy. Although the analysis is centered on two-layer GNNs with structural constraints on data, the insights are applicable to more general setups and justified by both synthetic and practical citation datasets.

Details

ICLR Conference 2023 Conference Paper

Min-Max Multi-objective Bilevel Optimization with Applications in Robust Machine Learning

  • Alex Gu
  • Songtao Lu
  • Parikshit Ram
  • Tsui-Wei Weng

We consider a generic min-max multi-objective bilevel optimization problem with applications in robust machine learning such as representation learning and hyperparameter optimization. We design MORBiT, a novel single-loop gradient descent-ascent bilevel optimization algorithm, to solve the generic problem and present a novel analysis showing that MORBiT converges to the first-order stationary point at a rate of $\widetilde{\mathcal{O}}(n^{1/2} K^{-2/5})$ for a class of weakly convex problems with $n$ objectives upon $K$ iterations of the algorithm. Our analysis utilizes novel results to handle the non-smooth min-max multi-objective setup and to obtain a sublinear dependence in the number of objectives $n$. Experimental results on robust representation learning and robust hyperparameter optimization showcase (i) the advantages of considering the min-max multi-objective setup, and (ii) convergence properties of the proposed \morbit.

Details

NeurIPS Conference 2023 Conference Paper

On the Convergence and Sample Complexity Analysis of Deep Q-Networks with $\epsilon$-Greedy Exploration

  • Shuai Zhang
  • Hongkang Li
  • Meng Wang
  • Miao Liu
  • Pin-Yu Chen
  • Songtao Lu
  • Sijia Liu
  • Keerthiram Murugesan

This paper provides a theoretical understanding of deep Q-Network (DQN) with the $\varepsilon$-greedy exploration in deep reinforcement learning. Despite the tremendous empirical achievement of the DQN, its theoretical characterization remains underexplored. First, the exploration strategy is either impractical or ignored in the existing analysis. Second, in contrast to conventional Q-learning algorithms, the DQN employs the target network and experience replay to acquire an unbiased estimation of the mean-square Bellman error (MSBE) utilized in training the Q-network. However, the existing theoretical analysis of DQNs lacks convergence analysis or bypasses the technical challenges by deploying a significantly overparameterized neural network, which is not computationally efficient. This paper provides the first theoretical convergence and sample complexity analysis of the practical setting of DQNs with $\epsilon$-greedy policy. We prove an iterative procedure with decaying $\epsilon$ converges to the optimal Q-value function geometrically. Moreover, a higher level of $\epsilon$ values enlarges the region of convergence but slows down the convergence, while the opposite holds for a lower level of $\epsilon$ values. Experiments justify our established theoretical insights on DQNs.

PDF Details

ICML Conference 2023 Conference Paper

Prometheus: Taming Sample and Communication Complexities in Constrained Decentralized Stochastic Bilevel Learning

  • Zhuqing Liu
  • Xin Zhang 0054
  • Prashant Khanduri
  • Songtao Lu
  • Jia Liu 0002

In recent years, decentralized bilevel optimization has gained significant attention thanks to its versatility in modeling a wide range of multi-agent learning problems, such as multi-agent reinforcement learning and multi-agent meta-learning. However, one unexplored and fundamental problem in this area is how to solve decentralized stochastic bilevel optimization problems with domain constraints while achieving low sample and communication complexities. This problem often arises from multi-agent learning problems with safety constraints. As shown in this paper, constrained decentralized bilevel optimization is far more challenging than its unconstrained counterpart due to the complex coupling structure, which necessitates new algorithm design and analysis techniques. Toward this end, we investigate a class of constrained decentralized bilevel optimization problems, where multiple agents collectively solve a nonconvex-strongly-convex bilevel problem with constraints in the upper-level variables. We propose an algorithm called Prometheus (proximal tracked stochastic recursive estimator) that achieves the first $\mathcal{O}(\epsilon^{-1})$ results in both sample and communication complexities for constrained decentralized bilevel optimization, where $\epsilon>0$ is a desired stationarity error. Collectively, the results in this work contribute to a theoretical foundation for low sample- and communication-complexity constrained decentralized bilevel learning.

Details

NeurIPS Conference 2023 Conference Paper

SLM: A Smoothed First-Order Lagrangian Method for Structured Constrained Nonconvex Optimization

  • Songtao Lu

Functional constrained optimization (FCO) has emerged as a powerful tool for solving various machine learning problems. However, with the rapid increase in applications of neural networks in recent years, it has become apparent that both the objective and constraints often involve nonconvex functions, which poses significant challenges in obtaining high-quality solutions. In this work, we focus on a class of nonconvex FCO problems with nonconvex constraints, where the two optimization variables are nonlinearly coupled in the inequality constraint. Leveraging the primal-dual optimization framework, we propose a smoothed first-order Lagrangian method (SLM) for solving this class of problems. We establish the theoretical convergence guarantees of SLM to the Karush-Kuhn-Tucker (KKT) solutions through quantifying dual error bounds. By establishing connections between this structured FCO and equilibrium-constrained nonconvex problems (also known as bilevel optimization), we apply the proposed SLM to tackle bilevel optimization oriented problems where the lower-level problem is nonconvex. Numerical results obtained from both toy examples and hyper-data cleaning problems demonstrate the superiority of SLM compared to benchmark methods.

PDF Details

ICML Conference 2022 Conference Paper

A Single-Loop Gradient Descent and Perturbed Ascent Algorithm for Nonconvex Functional Constrained Optimization

  • Songtao Lu

Nonconvex constrained optimization problems can be used to model a number of machine learning problems, such as multi-class Neyman-Pearson classification and constrained Markov decision processes. However, such kinds of problems are challenging because both the objective and constraints are possibly nonconvex, so it is difficult to balance the reduction of the loss value and reduction of constraint violation. Although there are a few methods that solve this class of problems, all of them are double-loop or triple-loop algorithms, and they require oracles to solve some subproblems up to certain accuracy by tuning multiple hyperparameters at each iteration. In this paper, we propose a novel gradient descent and perturbed ascent (GDPA) algorithm to solve a class of smooth nonconvex inequality constrained problems. The GDPA is a primal-dual algorithm, which only exploits the first-order information of both the objective and constraint functions to update the primal and dual variables in an alternating way. The key feature of the proposed algorithm is that it is a single-loop algorithm, where only two step-sizes need to be tuned. We show that under a mild regularity condition GDPA is able to find Karush-Kuhn-Tucker (KKT) points of nonconvex functional constrained problems with convergence rate guarantees. To the best of our knowledge, it is the first single-loop algorithm that can solve the general nonconvex smooth problems with nonconvex inequality constraints. Numerical results also showcase the superiority of GDPA compared with the best-known algorithms (in terms of both stationarity measure and feasibility of the obtained solutions).

Details

NeurIPS Conference 2022 Conference Paper

A Stochastic Linearized Augmented Lagrangian Method for Decentralized Bilevel Optimization

  • Songtao Lu
  • Siliang Zeng
  • Xiaodong Cui
  • Mark Squillante
  • Lior Horesh
  • Brian Kingsbury
  • Jia Liu
  • Mingyi Hong

Bilevel optimization has been shown to be a powerful framework for formulating multi-task machine learning problems, e. g. , reinforcement learning (RL) and meta-learning, where the decision variables are coupled in both levels of the minimization problems. In practice, the learning tasks would be located at different computing resource environments, and thus there is a need for deploying a decentralized training framework to implement multi-agent and multi-task learning. We develop a stochastic linearized augmented Lagrangian method (SLAM) for solving general nonconvex bilevel optimization problems over a graph, where both upper and lower optimization variables are able to achieve a consensus. We also establish that the theoretical convergence rate of the proposed SLAM to the Karush-Kuhn-Tucker (KKT) points of this class of problems is on the same order as the one achieved by the classical distributed stochastic gradient descent for only single-level nonconvex minimization problems. Numerical results tested on multi-agent RL problems showcase the superiority of SLAM compared with the benchmarks.

PDF Details

AAAI Conference 2022 Conference Paper

Adversarial Examples Can Be Effective Data Augmentation for Unsupervised Machine Learning

  • Chia-Yi Hsu
  • Pin-Yu Chen
  • Songtao Lu
  • Sijia Liu
  • Chia-Mu Yu

Adversarial examples causing evasive predictions are widely used to evaluate and improve the robustness of machine learning models. However, current studies focus on supervised learning tasks, relying on the ground-truth data label, a targeted objective, or supervision from a trained classifier. In this paper, we propose a framework of generating adversarial examples for unsupervised models and demonstrate novel applications to data augmentation. Our framework exploits a mutual information neural estimator as an information-theoretic similarity measure to generate adversarial examples without supervision. We propose a new MinMax algorithm with provable convergence guarantees for efficient generation of unsupervised adversarial examples. Our framework can also be extended to supervised adversarial examples. When using unsupervised adversarial examples as a simple plug-in data augmentation tool for model retraining, significant improvements are consistently observed across different unsupervised tasks and datasets, including data reconstruction, representation learning, and contrastive learning. Our results show novel methods and considerable advantages in studying and improving unsupervised machine learning via adversarial examples.

PDF Details

TIST Journal 2022 Journal Article

An Efficient Learning Framework for Federated XGBoost Using Secret Sharing and Distributed Optimization

  • Lunchen Xie
  • Jiaqi Liu
  • Songtao Lu
  • Tsung-Hui Chang
  • Qingjiang Shi

XGBoost is one of the most widely used machine learning models in the industry due to its superior learning accuracy and efficiency. Targeting at data isolation issues in the big data problems, it is crucial to deploy a secure and efficient federated XGBoost (FedXGB) model. Existing FedXGB models either have data leakage issues or are only applicable to the two-party setting with heavy communication and computation overheads. In this article, a lossless multi-party federated XGB learning framework is proposed with a security guarantee, which reshapes the XGBoost’s split criterion calculation process under a secret sharing setting and solves the leaf weight calculation problem by leveraging distributed optimization. Remarkably, a thorough analysis of model security is provided as well, and multiple numerical results showcase the superiority of the proposed FedXGB compared with the state-of-the-art models on benchmark datasets.

Details DOI

UAI Conference 2022 Conference Paper

Distributed adversarial training to robustify deep neural networks at scale

  • Gaoyuan Zhang
  • Songtao Lu
  • Yihua Zhang
  • Xiangyi Chen
  • Pin-Yu Chen
  • Quanfu Fan
  • Lee Martie
  • Lior Horesh

Current deep neural networks (DNNs) are vulnerable to adversarial attacks, where adversarial perturbations to the inputs can change or manipulate classification. To defend against such attacks, an effective and popular approach, known as adversarial training (AT), has been shown to mitigate the negative impact of adversarial attacks by virtue of a min-max robust training method. While effective, it remains unclear whether it can successfully be adapted to the distributed learning context. The power of distributed optimization over multiple machines enables us to scale up robust training over large models and datasets. Spurred by that, we propose distributed adversarial training (DAT), a large-batch adversarial training framework implemented over multiple machines. We show that DAT is general, which supports training over labeled and unlabeled data, multiple types of attack generation methods, and gradient compression operations favored for distributed optimization. Theoretically, we provide, under standard conditions in the optimization theory, the convergence rate of DAT to the first-order stationary points in general non-convex settings. Empirically, we demonstrate that DAT either matches or outperforms state-of-the-art robust accuracies and achieves a graceful training speedup (e. g. , on ResNet-50 under ImageNet). Codes are available at https: //github. com/dat-2022/dat.

Details

ICLR Conference 2022 Conference Paper

Finite-Time Convergence and Sample Complexity of Multi-Agent Actor-Critic Reinforcement Learning with Average Reward

  • Hairi
  • Jia Liu 0002
  • Songtao Lu

In this paper, we establish the first finite-time convergence result of the actor-critic algorithm for fully decentralized multi-agent reinforcement learning (MARL) problems with average reward. In this problem, a set of $N$ agents work cooperatively to maximize the global average reward through interacting with their neighbors over a communication network. We consider a practical MARL setting, where the rewards and actions of each agent are only known to itself, and the knowledge of joint actions of the agents is not assumed. Toward this end, we propose a mini-batch Markovian sampled fully decentralized actor-critic algorithm and analyze its finite-time convergence and sample complexity. We show that the sample complexity of this algorithm is $\mathcal{O}(N^{2}/\epsilon^{2}\log(N/\epsilon))$. Interestingly, this sample complexity bound matches that of the state-of-the-art single-agent actor-critic algorithms for reinforcement learning.

Details

IJCAI Conference 2022 Conference Paper

Learning to Generate Image Source-Agnostic Universal Adversarial Perturbations

  • Pu Zhao
  • Parikshit Ram
  • Songtao Lu
  • Yuguang Yao
  • Djallel Bouneffouf
  • Xue Lin
  • Sijia Liu

Adversarial perturbations are critical for certifying the robustness of deep learning models. A ``universal adversarial perturbation'' (UAP) can simultaneously attack multiple images, and thus offers a more unified threat model, obviating an image-wise attack algorithm. However, the existing UAP generator is underdeveloped when images are drawn from different image sources (e. g. , with different image resolutions). Towards an authentic universality across image sources, we take a novel view of UAP generation as a customized instance of ``few-shot learning'', which leverages bilevel optimization and learning-to-optimize (L2O) techniques for UAP generation with improved attack success rate (ASR). We begin by considering the popular model agnostic meta-learning (MAML) framework to meta-learn a UAP generator. However, we see that the MAML framework does not directly offer the universal attack across image sources, requiring us to integrate it with another meta-learning framework of L2O. The resulting scheme for meta-learning a UAP generator (i) has better performance (50% higher ASR) than baselines such as Projected Gradient Descent, (ii) has better performance (37% faster) than the vanilla L2O and MAML frameworks (when applicable), and (iii) is able to simultaneously handle UAP generation for different victim models and data sources.

PDF Details DOI

NeurIPS Conference 2022 Conference Paper

Understanding Benign Overfitting in Gradient-Based Meta Learning

  • Lisha Chen
  • Songtao Lu
  • Tianyi Chen

Meta learning has demonstrated tremendous success in few-shot learning with limited supervised data. In those settings, the meta model is usually overparameterized. While the conventional statistical learning theory suggests that overparameterized models tend to overfit, empirical evidence reveals that overparameterized meta learning methods still work well -- a phenomenon often called ``benign overfitting. '' To understand this phenomenon, we focus on the meta learning settings with a challenging bilevel structure that we term the gradient-based meta learning, and analyze its generalization performance under an overparameterized meta linear regression model. While our analysis uses the relatively tractable linear models, our theory contributes to understanding the delicate interplay among data heterogeneity, model adaptation and benign overfitting in gradient-based meta learning tasks. We corroborate our theoretical claims through numerical simulations.

PDF Details

ICLR Conference 2022 Conference Paper

Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspective

  • Qi Lyu
  • Xiao Fu 0001
  • Weiran Wang
  • Songtao Lu

Multiple views of data, both naturally acquired (e.g., image and audio) and artificially produced (e.g., via adding different noise to data samples), have proven useful in enhancing representation learning. Natural views are often handled by multiview analysis tools, e.g., (deep) canonical correlation analysis [(D)CCA], while the artificial ones are frequently used in self-supervised learning (SSL) paradigms, e.g., BYOL and Barlow Twins. Both types of approaches often involve learning neural feature extractors such that the embeddings of data exhibit high cross-view correlations. Although intuitive, the effectiveness of correlation-based neural embedding is mostly empirically validated. This work aims to understand latent correlation maximization-based deep multiview learning from a latent component identification viewpoint. An intuitive generative model of multiview data is adopted, where the views are different nonlinear mixtures of shared and private components. Since the shared components are view/distortion-invariant, representing the data using such components is believed to reveal the identity of the samples effectively and robustly. Under this model, latent correlation maximization is shown to guarantee the extraction of the shared components across views (up to certain ambiguities). In addition, it is further shown that the private information in each view can be provably disentangled from the shared using proper regularization design. A finite sample analysis, which has been rare in nonlinear mixture identifiability study, is also presented. The theoretical results and newly designed regularization are tested on a series of tasks.

Details

AAAI Conference 2022 Conference Paper

Zeroth-Order Optimization for Composite Problems with Functional Constraints

  • Zichong Li
  • Pin-Yu Chen
  • Sijia Liu
  • Songtao Lu
  • Yangyang Xu

In many real-world problems, first-order (FO) derivative evaluations are too expensive or even inaccessible. For solving these problems, zeroth-order (ZO) methods that only need function evaluations are often more efficient than FO methods or sometimes the only options. In this paper, we propose a novel zeroth-order inexact augmented Lagrangian method (ZO-iALM) to solve black-box optimization problems, which involve a composite (i. e. , smooth+nonsmooth) objective and functional constraints. This appears to be the first work that develops an iALM-based ZO method for functional constrained optimization and meanwhile achieves query complexity results matching the best-known FO complexity results up to a factor of variable dimension. With an extensive experimental study, we show the effectiveness of our method. The applications of our method span from classical optimization problems to practical machine learning examples such as resource allocation in sensor networks and adversarial example generation.

PDF Details

AAAI Conference 2021 Conference Paper

Decentralized Policy Gradient Descent Ascent for Safe Multi-Agent Reinforcement Learning

  • Songtao Lu
  • Kaiqing Zhang
  • Tianyi Chen
  • Tamer Başar
  • Lior Horesh

This paper deals with distributed reinforcement learning problems with safety constraints. In particular, we consider that a team of agents cooperate in a shared environment, where each agent has its individual reward function and safety constraints that involve all agents’ joint actions. As such, the agents aim to maximize the team-average long-term return, subject to all the safety constraints. More intriguingly, no central controller is assumed to coordinate the agents, and both the rewards and constraints are only known to each agent locally/privately. Instead, the agents are connected by a peer-to-peer communication network to share information with their neighbors. In this work, we first formulate this problem as a distributed constrained Markov decision process (D-CMDP) with networked agents. Then, we propose a decentralized policy gradient (PG) method, Safe Dec-PG, to perform policy optimization based on this D-CMDP model over a network. Convergence guarantees, together with numerical results, showcase the superiority of the proposed algorithm. To the best of our knowledge, this is the first decentralized PG algorithm that accounts for the coupled safety constraints with a quantifiable convergence rate in multi-agent reinforcement learning. Finally, we emphasize that our algorithm is also novel in solving a class of decentralized stochastic nonconvex-concave minimax optimization problems, where both the algorithm design and corresponding theoretical analysis are of independent interest.

PDF Details

NeurIPS Conference 2021 Conference Paper

Taming Communication and Sample Complexities in Decentralized Policy Evaluation for Cooperative Multi-Agent Reinforcement Learning

  • Xin Zhang
  • Zhuqing Liu
  • Jia Liu
  • Zhengyuan Zhu
  • Songtao Lu

Cooperative multi-agent reinforcement learning (MARL) has received increasing attention in recent years and has found many scientific and engineering applications. However, a key challenge arising from many cooperative MARL algorithm designs (e. g. , the actor-critic framework) is the policy evaluation problem, which can only be conducted in a {\em decentralized} fashion. In this paper, we focus on decentralized MARL policy evaluation with nonlinear function approximation, which is often seen in deep MARL. We first show that the empirical decentralized MARL policy evaluation problem can be reformulated as a decentralized nonconvex-strongly-concave minimax saddle point problem. We then develop a decentralized gradient-based descent ascent algorithm called GT-GDA that enjoys a convergence rate of $\mathcal{O}(1/T)$. To further reduce the sample complexity, we propose two decentralized stochastic optimization algorithms called GT-SRVR and GT-SRVRI, which enhance GT-GDA by variance reduction techniques. We show that all algorithms all enjoy an $\mathcal{O}(1/T)$ convergence rate to a stationary point of the reformulated minimax problem. Moreover, the fast convergence rates of GT-SRVR and GT-SRVRI imply $\mathcal{O}(\epsilon^{-2})$ communication complexity and $\mathcal{O}(m\sqrt{n}\epsilon^{-2})$ sample complexity, where $m$ is the number of agents and $n$ is the length of trajectories. To our knowledge, this paper is the first work that achieves both $\mathcal{O}(\epsilon^{-2})$ sample complexity and $\mathcal{O}(\epsilon^{-2})$ communication complexity in decentralized policy evaluation for cooperative MARL. Our extensive experiments also corroborate the theoretical performance of our proposed decentralized policy evaluation algorithms.

PDF Details

NeurIPS Conference 2020 Conference Paper

Decentralized TD Tracking with Linear Function Approximation and its Finite-Time Analysis

  • Gang Wang
  • Songtao Lu
  • Georgios Giannakis
  • Gerald Tesauro
  • Jian Sun

The present contribution deals with decentralized policy evaluation in multi-agent Markov decision processes using temporal-difference (TD) methods with linear function approximation for scalability. The agents cooperate to estimate the value function of such a process by observing continual state transitions of a shared environment over the graph of interconnected nodes (agents), along with locally private rewards. Different from existing consensus-type TD algorithms, the approach here develops a simple decentralized TD tracker by wedding TD learning with gradient tracking techniques. The non-asymptotic properties of the novel TD tracker are established for both independent and identically distributed (i. i. d. ) as well as Markovian transitions through a unifying multistep Lyapunov analysis. In contrast to the prior art, the novel algorithm forgoes the limiting error bounds on the number of agents, which endows it with performance comparable to that of centralized TD methods that are the sharpest known to date.

PDF Details

NeurIPS Conference 2020 Conference Paper

Finding Second-Order Stationary Points Efficiently in Smooth Nonconvex Linearly Constrained Optimization Problems

  • Songtao Lu
  • Meisam Razaviyayn
  • Bo Yang
  • Kejun Huang
  • Mingyi Hong

This paper proposes two efficient algorithms for computing approximate second-order stationary points (SOSPs) of problems with generic smooth non-convex objective functions and generic linear constraints. While finding (approximate) SOSPs for the class of smooth non-convex linearly constrained problems is computationally intractable, we show that generic problem instances in this class can be solved efficiently. Specifically, for a generic problem instance, we show that certain strict complementarity (SC) condition holds for all Karush-Kuhn-Tucker (KKT) solutions. Based on this condition, we design an algorithm named Successive Negative-curvature grAdient Projection (SNAP), which performs either conventional gradient projection or some negative curvature-based projection steps to find SOSPs. SNAP is a second-order algorithm that requires $\widetilde{\mathcal{O}}(\max\{1/\epsilon^2_G, 1/\epsilon^3_H\})$ iterations to compute an $(\epsilon_G, \epsilon_H)$-SOSP, where $\widetilde{\mathcal{O}}$ hides the iteration complexity for eigenvalue-decomposition. Building on SNAP, we propose a first-order algorithm, named SNAP$^+$, that requires $\mathcal{O}(1/\epsilon^{2. 5})$ iterations to compute $(\epsilon, \sqrt{\epsilon})$-SOSP. The per-iteration computational complexities of our algorithms are polynomial in the number of constraints and problem dimension. To the best of our knowledge, this is the first time that first-order algorithms with polynomial per-iteration complexity and global sublinear rate are designed to find SOSPs of the important class of non-convex problems with linear constraints (almost surely).

PDF Details

ICML Conference 2020 Conference Paper

Improving the Sample and Communication Complexity for Decentralized Non-Convex Optimization: Joint Gradient Estimation and Tracking

  • Haoran Sun
  • Songtao Lu
  • Mingyi Hong 0001

Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and local stochastic gradient estimates can outperform state-of-the-art centralized algorithms, in applications involving highly non-convex problems, such as training deep neural networks. In this work, we propose a decentralized stochastic algorithm to deal with certain smooth non-convex problems where there are $m$ nodes in the system, and each node has a large number of samples (denoted as $n$). Differently from the majority of the existing decentralized learning algorithms for either stochastic or finite-sum problems, our focus is given to \emph{both} reducing the total communication rounds among the nodes, while accessing the minimum number of local data samples. In particular, we propose an algorithm named D-GET (decentralized gradient estimation and tracking), which jointly performs decentralized gradient estimation (which estimates the local gradient using a subset of local samples) \emph{and} gradient tracking (which tracks the global full gradient using local estimates). We show that to achieve certain $\epsilon$ stationary solution of the deterministic finite sum problem, the proposed algorithm achieves an $\mathcal{O}(mn^{1/2}\epsilon^{-1})$ sample complexity and an $\mathcal{O}(\epsilon^{-1})$ communication complexity. These bounds significantly improve upon the best existing bounds of $\mathcal{O}(mn\epsilon^{-1})$ and $\mathcal{O}(\epsilon^{-1})$, respectively. Similarly, for online problems, the proposed method achieves an $\mathcal{O}(m \epsilon^{-3/2})$ sample complexity and an $\mathcal{O}(\epsilon^{-1})$ communication complexity.

Details

ICML Conference 2020 Conference Paper

Min-Max Optimization without Gradients: Convergence and Applications to Black-Box Evasion and Poisoning Attacks

  • Sijia Liu 0001
  • Songtao Lu
  • Xiangyi Chen
  • Yao Feng 0002
  • Kaidi Xu
  • Abdullah Al-Dujaili
  • Mingyi Hong 0001
  • Una-May O'Reilly

In this paper, we study the problem of constrained min-max optimization in a black-box setting, where the desired optimizer cannot access the gradients of the objective function but may query its values. We present a principled optimization framework, integrating a zeroth-order (ZO) gradient estimator with an alternating projected stochastic gradient descent-ascent method, where the former only requires a small number of function queries and the later needs just one-step descent/ascent update. We show that the proposed framework, referred to as ZO-Min-Max, has a sublinear convergence rate under mild conditions and scales gracefully with problem size. We also explore a promising connection between black-box min-max optimization and black-box evasion and poisoning attacks in adversarial machine learning (ML). Our empirical evaluations on these use cases demonstrate the effectiveness of our approach and its scalability to dimensions that prohibit using recent black-box solvers.

Details

NeurIPS Conference 2020 Conference Paper

ScaleCom: Scalable Sparsified Gradient Compression for Communication-Efficient Distributed Training

  • Chia-Yu Chen
  • Jiamin Ni
  • Songtao Lu
  • Xiaodong Cui
  • Pin-Yu Chen
  • Xiao Sun
  • Naigang Wang
  • Swagath Venkataramani

Large-scale distributed training of Deep Neural Networks (DNNs) on state-of-the-art platforms are expected to be severely communication constrained. To overcome this limitation, numerous gradient compression techniques have been proposed and have demonstrated high compression ratios. However, most existing compression methods do not scale well to large scale distributed systems (due to gradient build-up) and / or lack evaluations in large datasets. To mitigate these issues, we propose a new compression technique, Scalable Sparsified Gradient Compression (ScaleComp), that (i) leverages similarity in the gradient distribution amongst learners to provide a commutative compressor and keep communication cost constant to worker number and (ii) includes low-pass filter in local gradient accumulations to mitigate the impacts of large batch size training and significantly improve scalability. Using theoretical analysis, we show that ScaleComp provides favorable convergence guarantees and is compatible with gradient all-reduce techniques. Furthermore, we experimentally demonstrate that ScaleComp has small overheads, directly reduces gradient traffic and provides high compression rates (70-150X) and excellent scalability (up to 64-80 learners and 10X larger batch sizes over normal training) across a wide range of applications (image, language, and speech) without significant accuracy loss.

PDF Details

ICML Conference 2019 Conference Paper

PA-GD: On the Convergence of Perturbed Alternating Gradient Descent to Second-Order Stationary Points for Structured Nonconvex Optimization

  • Songtao Lu
  • Mingyi Hong 0001
  • Zhengdao Wang

Alternating gradient descent (A-GD) is a simple but popular algorithm in machine learning, which updates two blocks of variables in an alternating manner using gradient descent steps. In this paper, we consider a smooth unconstrained nonconvex optimization problem, and propose a perturbed A-GD (PA-GD) which is able to converge (with high probability) to the second-order stationary points (SOSPs) with a global sublinear rate. Existing analysis on A-GD type algorithm either only guarantees convergence to first-order solutions, or converges to second-order solutions asymptotically (without rates). To the best of our knowledge, this is the first alternating type algorithm that takes $\mathcal{O}(\text{polylog}(d)/\epsilon^2)$ iterations to achieve an ($\epsilon, \sqrt{\epsilon}$)-SOSP with high probability, where polylog$(d)$ denotes the polynomial of the logarithm with respect to problem dimension $d$.

Details
v2026.09.13