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Dongruo Zhou

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36

TMLR Journal 2026 Journal Article

Return Augmented Decision Transformer for Off-Dynamics Reinforcement Learning

  • Ruhan Wang
  • Yu Yang
  • Zhishuai Liu
  • Dongruo Zhou
  • Pan Xu

We study offline off-dynamics reinforcement learning (RL) to utilize data from an easily accessible source domain to enhance policy learning in a target domain with limited data. Our approach centers on return-conditioned supervised learning (RCSL), particularly focusing on Decision Transformer (DT) type frameworks, which can predict actions conditioned on desired return guidance and complete trajectory history. Previous works address the dynamics shift problem by augmenting the reward in the trajectory from the source domain to match the optimal trajectory in the target domain. However, this strategy can not be directly applicable in RCSL owing to (1) the unique form of the RCSL policy class, which explicitly depends on the return, and (2) the absence of a straightforward representation of the optimal trajectory distribution. We propose the Return Augmented (REAG) method for DT type frameworks, where we augment the return in the source domain by aligning its distribution with that in the target domain. We provide the theoretical analysis demonstrating that the RCSL policy learned from REAG achieves the same level of suboptimality as would be obtained without a dynamics shift. We introduce two practical implementations $REAG^{∗}_{Dara}$ and $REAG^{∗}_{MV}$ respectively. Thorough experiments on D4RL datasets and various DT-type baselines demonstrate that our methods consistently enhance the performance of DT type frameworks in off-dynamics RL.

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ICLR Conference 2025 Conference Paper

Breaking the log⁡(1/Δ2) Barrier: Better Batched Best Arm Identification with Adaptive Grids

  • Tianyuan Jin
  • Qin Zhang 0001
  • Dongruo Zhou

We investigate the problem of batched best arm identification in multi-armed bandits, where we want to find the best arm from a set of $n$ arms while minimizing both the number of samples and batches. We introduce an algorithm that achieves near-optimal sample complexity and features an instance-sensitive batch complexity, which breaks the $\log(1/\Delta_2)$ barrier. The main contribution of our algorithm is a novel sample allocation scheme that effectively balances exploration and exploitation for batch sizes. Experimental results indicate that our approach is more batch-efficient across various setups. We also extend this framework to the problem of batched best arm identification in linear bandits and achieve similar improvements.

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ICML Conference 2025 Conference Paper

Federated In-Context Learning: Iterative Refinement for Improved Answer Quality

  • Ruhan Wang
  • Zhiyong Wang
  • Chengkai Huang
  • Rui Wang
  • Tong Yu 0001
  • Lina Yao 0001
  • John C. S. Lui
  • Dongruo Zhou

For question-answering (QA) tasks, in-context learning (ICL) enables language models (LMs) to generate responses without modifying their parameters by leveraging examples provided in the input. However, the effectiveness of ICL heavily depends on the availability of high-quality examples, which are often scarce due to data privacy constraints, annotation costs, and distribution disparities. A natural solution is to utilize examples stored on client devices, but existing approaches either require transmitting model parameters—incurring significant communication overhead—or fail to fully exploit local datasets, limiting their effectiveness. To address these challenges, we propose Federated In-Context Learning (Fed-ICL), a general framework that enhances ICL through an iterative, collaborative process. Fed-ICL progressively refines responses by leveraging multi-round interactions between clients and a central server, improving answer quality without the need to transmit model parameters. We establish theoretical guarantees for the convergence of Fed-ICL and conduct extensive experiments on standard QA benchmarks, demonstrating that our proposed approach achieves strong performance while maintaining low communication costs.

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ICLR Conference 2025 Conference Paper

Model-based RL as a Minimalist Approach to Horizon-Free and Second-Order Bounds

  • Zhiyong Wang
  • Dongruo Zhou
  • John C. S. Lui
  • Wen Sun 0002

Learning a transition model via Maximum Likelihood Estimation (MLE) followed by planning inside the learned model is perhaps the most standard and simplest Model-based Reinforcement Learning (RL) framework. In this work, we show that such a simple Model-based RL scheme, when equipped with optimistic and pessimistic planning procedures, achieves strong regret and sample complexity bounds in online and offline RL settings. Particularly, we demonstrate that under the conditions where the trajectory-wise reward is normalized between zero and one and the transition is time-homogenous, it achieves nearly horizon-free and second-order bounds.

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ICML Conference 2025 Conference Paper

Provable Zero-Shot Generalization in Offline Reinforcement Learning

  • Zhiyong Wang
  • Chen Yang
  • John C. S. Lui
  • Dongruo Zhou

In this work, we study offline reinforcement learning (RL) with zero-shot generalization property (ZSG), where the agent has access to an offline dataset including experiences from different environments, and the goal of the agent is to train a policy over the training environments which performs well on test environments without further interaction. Existing work showed that classical offline RL fails to generalize to new, unseen environments. We propose pessimistic empirical risk minimization (PERM) and pessimistic proximal policy optimization (PPPO), which leverage pessimistic policy evaluation to guide policy learning and enhance generalization. We show that both PERM and PPPO are capable of finding a near-optimal policy with ZSG. Our result serves as a first step in understanding the foundation of the generalization phenomenon in offline reinforcement learning.

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UAI Conference 2025 Conference Paper

Sample and Computationally Efficient Continuous-Time Reinforcement Learning with General Function Approximation

  • Runze Zhao
  • Yue Yu
  • Adams Yiyue Zhu
  • Chen Yang
  • Dongruo Zhou

Continuous-time reinforcement learning (CTRL) provides a principled framework for sequential decision-making in environments where interactions evolve continuously over time. Despite its empirical success, the theoretical understanding of CTRL remains limited, especially in settings with general function approximation. In this work, we propose a model-based CTRL algorithm that achieves both sample and computational efficiency. Our approach leverages optimism-based confidence sets to establish the first sample complexity guarantee for CTRL with general function approximation, showing that a near-optimal policy can be learned with a suboptimality gap of $\tilde{O}(\sqrt{d_{\mathcal{R}} + d_{\mathcal{F}}}N^{-1/2})$ using $N$ measurements, where $d_{\mathcal{R}}$ and $d_{\mathcal{F}}$ denote the distributional Eluder dimensions of the reward and dynamic functions, respectively, capturing the complexity of general function approximation in reinforcement learning. Moreover, we introduce structured policy updates and an alternative measurement strategy that significantly reduce the number of policy updates and rollouts while maintaining competitive sample efficiency. Our proposed algorithms are validated through experiments on continuous control tasks and diffusion model fine-tuning, demonstrating comparable performance with significantly fewer policy updates and rollouts.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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 $H \ge d$.

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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.

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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.

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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.

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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.

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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.

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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 )

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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.

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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 )

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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.

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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.

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