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Chen-Yu Wei

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29 papers
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29

NeurIPS Conference 2025 Conference Paper

An Improved Algorithm for Adversarial Linear Contextual Bandits via Reduction

  • Tim van Erven
  • Jack Mayo
  • Julia Olkhovskaya
  • Chen-Yu Wei

We present an efficient algorithm for linear contextual bandits with adversarial losses and stochastic action sets. Our approach reduces this setting to misspecification-robust adversarial linear bandits with fixed action sets. Without knowledge of the context distribution or access to a context simulator, the algorithm achieves $\tilde{O}(\min\{d^2\sqrt{T}, \sqrt{d^3T\log K}\})$ regret and runs in $\mathrm{poly}(d, C, T)$ time, where $d$ is the feature dimension, $C$ is an upper bound on the number of linear constraints defining the action set in each round, $K$ is an upper bound on the number of actions in each round, and $T$ is number of rounds. This resolves the open question by Liu et al. (2023) on whether one can obtain $\mathrm{poly}(d)\sqrt{T}$ regret in polynomial time independent of the number of actions. For the important class of combinatorial bandits with adversarial losses and stochastic action sets where the action sets can be described by a polynomial number of linear constraints, our algorithm is the first to achieve $\mathrm{poly}(d)\sqrt{T}$ regret in polynomial time, while no prior algorithm achieves even $o(T)$ regret in polynomial time to our knowledge. When a simulator is available, the regret bound can be improved to $\tilde{O}(d\sqrt{L^\star})$, where $L^\star$ is the cumulative loss of the best policy.

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NeurIPS Conference 2025 Conference Paper

From Average-Iterate to Last-Iterate Convergence in Games: A Reduction and Its Applications

  • Yang Cai
  • Haipeng Luo
  • Chen-Yu Wei
  • Weiqiang Zheng

The convergence of online learning algorithms in games under self-play is a fundamental question in game theory and machine learning. Among various notions of convergence, last-iterate convergence is particularly desirable, as it reflects the actual decisions made by the learners and captures the day-to-day behavior of the learning dynamics. While many algorithms are known to converge in the average-iterate, achieving last-iterate convergence typically requires considerably more effort in both the design and the analysis of the algorithm. Somewhat surprisingly, we show in this paper that for a large family of games, there exists a simple black-box reduction that transforms the average iterates of an uncoupled learning dynamics into the last iterates of a new uncoupled learning dynamics, thus also providing a reduction from last-iterate convergence to average-iterate convergence. Our reduction applies to games where each player’s utility is linear in both their own strategy and the joint strategy of all opponents. This family includes two-player bimatrix games and generalizations such as multi-player polymatrix games. By applying our reduction to the Optimistic Multiplicative Weights Update algorithm, we obtain new state-of-the-art last-iterate convergence rates for uncoupled learning dynamics in multi-player zero-sum polymatrix games: (1) an $O(\frac{\log d}{T})$ last-iterate convergence rate under gradient feedback, representing an exponential improvement in the dependence on the dimension $d$ (i. e. , the maximum number of actions available to either player); and (2) an $\tilde{O}(d^{\frac{1}{5}}T^{-\frac{1}{5}})$ last-iterate convergence rate under bandit feedback, improving upon the previous best rates of $\tilde{O}(\sqrt{d}T^{-\frac{1}{8}})$ and $\tilde{O}(\sqrt{d}T^{-\frac{1}{6}})$.

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RLJ Journal 2025 Journal Article

HANQ: Hypergradients, Asymmetry, and Normalization for Fast and Stable Deep $Q$-Learning

  • Braham Snyder
  • Chen-Yu Wei

In reinforcement learning (RL), deep \$Q\$-learning algorithms are often more sample- and compute-efficient than alternatives like the Monte Carlo policy gradient, but tend to suffer from instability that limits their use in practice. Some of this instability can be mitigated through a delayed *target network*, yet this doubles memory usage and arguably slows down convergence. In this work, we explore the possibility of stabilization (returns do not drop with further gradient steps) without sacrificing the speed of convergence (high returns do not require many gradient steps). Inspired by self-supervised learning (SSL) and adaptive optimization, we empirically arrive at three modifications to the standard deep \$Q\$-network (DQN) — no two of which work well alone in our experiments. These modifications are, in the order of our experiments: 1) an **A**symmetric *predictor* in the neural network, 2) a particular combination of **N**ormalization layers, and 3) **H**ypergradient descent on the learning rate. Aligning with prior work in SSL, **HANQ** (pronounced ""*hank*"") avoids DQN's target network, uses the same number of hyperparameters as DQN, and yet matches or exceeds DQN's performance in our offline RL experiments on three out of four environments.

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RLC Conference 2025 Conference Paper

HANQ: Hypergradients, Asymmetry, and Normalization for Fast and Stable Deep $Q$-Learning

  • Braham Snyder
  • Chen-Yu Wei

In reinforcement learning (RL), deep \$Q\$-learning algorithms are often more sample- and compute-efficient than alternatives like the Monte Carlo policy gradient, but tend to suffer from instability that limits their use in practice. Some of this instability can be mitigated through a delayed *target network*, yet this doubles memory usage and arguably slows down convergence. In this work, we explore the possibility of stabilization (returns do not drop with further gradient steps) without sacrificing the speed of convergence (high returns do not require many gradient steps). Inspired by self-supervised learning (SSL) and adaptive optimization, we empirically arrive at three modifications to the standard deep \$Q\$-network (DQN) — no two of which work well alone in our experiments. These modifications are, in the order of our experiments: 1) an **A**symmetric *predictor* in the neural network, 2) a particular combination of **N**ormalization layers, and 3) **H**ypergradient descent on the learning rate. Aligning with prior work in SSL, **HANQ** (pronounced ""*hank*"") avoids DQN's target network, uses the same number of hyperparameters as DQN, and yet matches or exceeds DQN's performance in our offline RL experiments on three out of four environments.

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NeurIPS Conference 2024 Conference Paper

Beating Adversarial Low-Rank MDPs with Unknown Transition and Bandit Feedback

  • Haolin Liu
  • Zakaria Mhammedi
  • Chen-Yu Wei
  • Julian Zimmert

We consider regret minimization in low-rank MDPs with fixed transition and adversarial losses. Previous work has investigated this problem under either full-information loss feedback with unknown transitions (Zhao et al. , 2024), or bandit loss feedback with known transitions (Foster et al. , 2022). First, we improve the $poly(d, A, H)T^{5/6}$ regret bound of Zhao et al. (2024) to $poly(d, A, H)T^{2/3}$ for the full-information unknown transition setting, where $d$ is the rank of the transitions, $A$ is the number of actions, $H$ is the horizon length, and $T$ is the number of episodes. Next, we initiate the study on the setting with bandit loss feedback and unknown transitions. Assuming that the loss has a linear structure, we propose both model-based and model-free algorithms achieving $poly(d, A, H)T^{2/3}$ regret, though they are computationally inefficient. We also propose oracle-efficient model-free algorithms with $poly(d, A, H)T^{4/5}$ regret. We show that the linear structure is necessary for the bandit case—without structure on the reward function, the regret has to scale polynomially with the number of states. This is contrary to the full-information case (Zhao et al. , 2024), where the regret can be independent of the number of states even for unstructured reward functions.

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NeurIPS Conference 2024 Conference Paper

Corruption-Robust Linear Bandits: Minimax Optimality and Gap-Dependent Misspecification

  • Haolin Liu
  • Artin Tajdini
  • Andrew Wagenmaker
  • Chen-Yu Wei

In linear bandits, how can a learner effectively learn when facing corrupted rewards? While significant work has explored this question, a holistic understanding across different adversarial models and corruption measures is lacking, as is a full characterization of the minimax regret bounds. In this work, we compare two types of corruptions commonly considered: strong corruption, where the corruption level depends on the learner’s chosen action, and weak corruption, where the corruption level does not depend on the learner’s chosen action. We provide a unified framework to analyze these corruptions. For stochastic linear bandits, we fully characterize the gap between the minimax regret under strong and weak corruptions. We also initiate the study of corrupted adversarial linear bandits, obtaining upper and lower bounds with matching dependencies on the corruption level. Next, we reveal a connection between corruption-robust learning and learning with gap-dependent misspecification—a setting first studied by Liu et al. (2023a), where the misspecification level of an action or policy is proportional to its suboptimality. We present a general reduction that enables any corruption-robust algorithm to handle gap-dependent misspecification. This allows us to recover the results of Liu et al. (2023a) in a black-box manner and significantly generalize them to settings like linear MDPs, yielding the first results for gap-dependent misspecification in reinforcement learning. However, this general reduction does not attain the optimal rate for gap-dependent misspecification. Motivated by this, we develop a specialized algorithm that achieves optimal bounds for gap-dependent misspecification in linear bandits, thus answering an open question posed by Liu et al. (2023a).

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NeurIPS Conference 2024 Conference Paper

How Does Variance Shape the Regret in Contextual Bandits?

  • Zeyu Jia
  • Jian Qian
  • Alexander Rakhlin
  • Chen-Yu Wei

We consider realizable contextual bandits with general function approximation, investigating how small reward variance can lead to better-than-minimax regret bounds. Unlike in minimax regret bounds, we show that the eluder dimension $d_{\text{elu}}$$-$a measure of the complexity of the function class$-$plays a crucial role in variance-dependent bounds. We consider two types of adversary: (1) Weak adversary: The adversary sets the reward variance before observing the learner's action. In this setting, we prove that a regret of $\Omega( \sqrt{ \min (A, d_{\text{elu}}) \Lambda } + d_{\text{elu}} )$ is unavoidable when $d_{\text{elu}} \leq \sqrt{A T}$, where $A$ is the number of actions, $T$ is the total number of rounds, and $\Lambda$ is the total variance over $T$ rounds. For the $A\leq d_{\text{elu}}$ regime, we derive a nearly matching upper bound $\tilde{O}( \sqrt{ A\Lambda } + d_{\text{elu} } )$ for the special case where the variance is revealed at the beginning of each round. (2) Strong adversary: The adversary sets the reward variance after observing the learner's action. We show that a regret of $\Omega( \sqrt{ d_{\text{elu}} \Lambda } + d_{\text{elu}} )$ is unavoidable when $\sqrt{ d_{\text{elu}} \Lambda } + d_{\text{elu}} \leq \sqrt{A T}$. In this setting, we provide an upper bound of order $\tilde{O}( d_{\text{elu}}\sqrt{ \Lambda } + d_{\text{elu}} )$. Furthermore, we examine the setting where the function class additionally provides distributional information of the reward, as studied by Wang et al. (2024). We demonstrate that the regret bound $\tilde{O}(\sqrt{d_{\text{elu}} \Lambda} + d_{\text{elu}})$ established in their work is unimprovable when $\sqrt{d_{\text{elu}} \Lambda} + d_{\text{elu}}\leq \sqrt{AT}$. However, with a slightly different definition of the total variance and with the assumption that the reward follows a Gaussian distribution, one can achieve a regret of $\tilde{O}(\sqrt{A\Lambda} + d_{\text{elu}})$.

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NeurIPS Conference 2024 Conference Paper

On Tractable $\Phi$-Equilibria in Non-Concave Games

  • Yang Cai
  • Constantinos Daskalakis
  • Haipeng Luo
  • Chen-Yu Wei
  • Weiqiang Zheng

While Online Gradient Descent and other no-regret learning procedures are known to efficiently converge to a coarse correlated equilibrium in games where each agent's utility is concave in their own strategy, this is not the case when utilities are non-concave -- a common scenario in machine learning applications involving strategies parameterized by deep neural networks, or when agents' utilities are computed by neural networks, or both. Non-concave games introduce significant game-theoretic and optimization challenges: (i) Nash equilibria may not exist; (ii) local Nash equilibria, though they exist, are intractable; and (iii) mixed Nash, correlated, and coarse correlated equilibria generally have infinite support and are intractable. To sidestep these challenges, we revisit the classical solution concept of $\Phi$-equilibria introduced by Greenwald and Jafari [GJ03], which is guaranteed to exist for an arbitrary set of strategy modifications $\Phi$ even in non-concave games [SL07]. However, the tractability of $\Phi$-equilibria in such games remains elusive. In this paper, we initiate the study of tractable $\Phi$-equilibria in non-concave games and examine several natural families of strategy modifications. We show that when $\Phi$ is finite, there exists an efficient uncoupled learning algorithm that approximates the corresponding $\Phi$-equilibria. Additionally, we explore cases where $\Phi$ is infinite but consists of local modifications, showing that Online Gradient Descent can efficiently approximate $\Phi$-equilibria in non-trivial regimes.

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ICLR Conference 2024 Conference Paper

Towards Optimal Regret in Adversarial Linear MDPs with Bandit Feedback

  • Haolin Liu
  • Chen-Yu Wei
  • Julian Zimmert

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback. We introduce two algorithms that achieve improved regret performance compared to existing approaches. The first algorithm, although computationally inefficient, achieves a regret of $\widetilde{O}(\sqrt{K})$ without relying on simulators, where $K$ is the number of episodes. This is the first rate-optimal result in the considered setting. The second algorithm is computationally efficient and achieves a regret of $\widetilde{O}(K^{\frac{3}{4}})$ . These results significantly improve over the prior state-of-the-art: a computationally inefficient algorithm by Kong et al. (2023) with $\widetilde{O}(K^{\frac{4}{5}}+1/\lambda_{\min})$ regret, and a computationally efficient algorithm by Sherman et al. (2023b) with $\widetilde{O}(K^{\frac{6}{7}})$ regret.

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ICML Conference 2023 Conference Paper

Best of Both Worlds Policy Optimization

  • Christoph Dann
  • Chen-Yu Wei
  • Julian Zimmert

Policy optimization methods are popular reinforcement learning algorithms in practice and recent works have build theoretical foundation for them by proving $\sqrt{T}$ regret bounds even when the losses are adversarial. Such bounds are tight in the worst case but often overly pessimistic. In this work, we show that by carefully designing the regularizer, bonus terms, and learning rates, one can achieve a more favorable $\text{polylog}(T)$ regret bound when the losses are stochastic, without sacrificing the worst-case guarantee in the adversarial regime. Specifically, we show the first best of both worlds guarantee for policy optimization in tabular MDPs by leveraging either a Tsallis entropy or a Shannon entropy regularizer. Then we show that under known transitions, we can further obtain a first-order regret bound in the adversarial regime by leveraging the log barrier regularizer.

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NeurIPS Conference 2023 Conference Paper

Bypassing the Simulator: Near-Optimal Adversarial Linear Contextual Bandits

  • Haolin Liu
  • Chen-Yu Wei
  • Julian Zimmert

We consider the adversarial linear contextual bandit problem, where the loss vectors are selected fully adversarially and the per-round action set (i. e. the context) is drawn from a fixed distribution. Existing methods for this problem either require access to a simulator to generate free i. i. d. contexts, achieve a sub-optimal regret no better than $\tilde{\mathcal{O}}(T^{\frac{5}{6}})$, or are computationally inefficient. We greatly improve these results by achieving a regret of $\tilde{\mathcal{O}}(\sqrt{T})$ without a simulator, while maintaining computational efficiency when the action set in each round is small. In the special case of sleeping bandits with adversarial loss and stochastic arm availability, our result answers affirmatively the open question by [SGV20] on whether there exists a polynomial-time algorithm with $poly(d)\sqrt{T}$ regret. Our approach naturally handles the case where the loss is linear up to an additive misspecification error, and our regret shows near-optimal dependence on the magnitude of the error.

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NeurIPS Conference 2023 Conference Paper

First- and Second-Order Bounds for Adversarial Linear Contextual Bandits

  • Julia Olkhovskaya
  • Jack Mayo
  • Tim van Erven
  • Gergely Neu
  • Chen-Yu Wei

We consider the adversarial linear contextual bandit setting, whichallows for the loss functions associated with each of $K$ arms to changeover time without restriction. Assuming the $d$-dimensional contexts aredrawn from a fixed known distribution, the worst-case expected regretover the course of $T$ rounds is known to scale as $\tilde O(\sqrt{KdT})$. Under the additional assumption that the density of the contextsis log-concave, we obtain a second-order bound of order $\tildeO(K\sqrt{d V_T})$ in terms of the cumulative second moment of thelearner's losses $V_T$, and a closely related first-order bound of order$\tilde O(K\sqrt{d L_T^*})$ in terms of the cumulative loss of the bestpolicy $L_T^*$. Since $V_T$ or $L_T^*$ may be significantly smaller than$T$, these improve over the worst-case regret whenever the environmentis relatively benign. Our results are obtained using a truncated versionof the continuous exponential weights algorithm over the probabilitysimplex, which we analyse by exploiting a novel connection to the linearbandit setting without contexts.

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EWRL Workshop 2023 Workshop Paper

First- and Second-Order Bounds for Adversarial Linear Contextual Bandits

  • Julia Olkhovskaya
  • Jack Mayo
  • Tim van Erven
  • Gergely Neu
  • Chen-Yu Wei

We consider the adversarial linear contextual bandit setting, which allows for the loss functions associated with each of $K$ arms to change over time without restriction. Assuming the $d$-dimensional contexts are drawn from a fixed known distribution, the worst-case expected regret over the course of $T$ rounds is known to scale as $\tilde O(\sqrt{KdT})$. Under the additional assumption that the density of the contexts is log-concave, we obtain a second-order bound of order $\tilde O(K\sqrt{d V_T})$ in terms of the cumulative second moment of the learner's losses $V_T$, and a closely related first-order bound of order $\tilde O(K\sqrt{d L_T^*})$ in terms of the cumulative loss of the best policy $L_T^*$. Since $V_T$ or $L_T^*$ may be significantly smaller than $T$, these improve over the worst-case regret whenever the environment is relatively benign. Our results are obtained using a truncated version of the continuous exponential weights algorithm over the probability simplex, which we analyse by exploiting a novel connection to the linear bandit setting without contexts.

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NeurIPS Conference 2023 Conference Paper

Last-Iterate Convergent Policy Gradient Primal-Dual Methods for Constrained MDPs

  • Dongsheng Ding
  • Chen-Yu Wei
  • Kaiqing Zhang
  • Alejandro Ribeiro

We study the problem of computing an optimal policy of an infinite-horizon discounted constrained Markov decision process (constrained MDP). Despite the popularity of Lagrangian-based policy search methods used in practice, the oscillation of policy iterates in these methods has not been fully understood, bringing out issues such as violation of constraints and sensitivity to hyper-parameters. To fill this gap, we employ the Lagrangian method to cast a constrained MDP into a constrained saddle-point problem in which max/min players correspond to primal/dual variables, respectively, and develop two single-time-scale policy-based primal-dual algorithms with non-asymptotic convergence of their policy iterates to an optimal constrained policy. Specifically, we first propose a regularized policy gradient primal-dual (RPG-PD) method that updates the policy using an entropy-regularized policy gradient, and the dual variable via a quadratic-regularized gradient ascent, simultaneously. We prove that the policy primal-dual iterates of RPG-PD converge to a regularized saddle point with a sublinear rate, while the policy iterates converge sublinearly to an optimal constrained policy. We further instantiate RPG-PD in large state or action spaces by including function approximation in policy parametrization, and establish similar sublinear last-iterate policy convergence. Second, we propose an optimistic policy gradient primal-dual (OPG-PD) method that employs the optimistic gradient method to update primal/dual variables, simultaneously. We prove that the policy primal-dual iterates of OPG-PD converge to a saddle point that contains an optimal constrained policy, with a linear rate. To the best of our knowledge, this work appears to be the first non-asymptotic policy last-iterate convergence result for single-time-scale algorithms in constrained MDPs. We further validate the merits and the effectiveness of our methods in computational experiments.

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NeurIPS Conference 2023 Conference Paper

No-Regret Online Reinforcement Learning with Adversarial Losses and Transitions

  • Tiancheng Jin
  • Junyan Liu
  • Chloé Rouyer
  • William Chang
  • Chen-Yu Wei
  • Haipeng Luo

Existing online learning algorithms for adversarial Markov Decision Processes achieve $\mathcal{O}(\sqrt{T})$ regret after $T$ rounds of interactions even if the loss functions are chosen arbitrarily by an adversary, with the caveat that the transition function has to be fixed. This is because it has been shown that adversarial transition functions make no-regret learning impossible. Despite such impossibility results, in this work, we develop algorithms that can handle both adversarial losses and adversarial transitions, with regret increasing smoothly in the degree of maliciousness of the adversary. More concretely, we first propose an algorithm that enjoys $\widetilde{\mathcal{O}}(\sqrt{T} + C^{P})$ regret where $C^{P}$ measures how adversarial the transition functions are and can be at most $\mathcal{O}(T)$. While this algorithm itself requires knowledge of $C^{P}$, we further develop a black-box reduction approach that removes this requirement. Moreover, we also show that further refinements of the algorithm not only maintains the same regret bound, but also simultaneously adapts to easier environments (where losses are generated in a certain stochastically constrained manner as in [Jin et al. 2021]) and achieves $\widetilde{\mathcal{O}}(U + \sqrt{UC^{L}} + C^{P})$ regret, where $U$ is some standard gap-dependent coefficient and $C^{L}$ is the amount of corruption on losses.

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ICML Conference 2023 Conference Paper

Refined Regret for Adversarial MDPs with Linear Function Approximation

  • Yan Dai 0002
  • Haipeng Luo
  • Chen-Yu Wei
  • Julian Zimmert

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over $K$ episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in some known features, that is, a linear function approximation exists. The best existing regret upper bound for this setting (Luo et al. , 2021) is of order $\tilde{\mathcal O}(K^{2/3})$ (omitting all other dependencies), given access to a simulator. This paper provides two algorithms that improve the regret to $\tilde{\mathcal O}(\sqrt K)$ in the same setting. Our first algorithm makes use of a refined analysis of the Follow-the-Regularized-Leader (FTRL) algorithm with the log-barrier regularizer. This analysis allows the loss estimators to be arbitrarily negative and might be of independent interest. Our second algorithm develops a magnitude-reduced loss estimator, further removing the polynomial dependency on the number of actions in the first algorithm and leading to the optimal regret bound (up to logarithmic terms and dependency on the horizon). Moreover, we also extend the first algorithm to simulator-free linear MDPs, which achieves $\tilde{\mathcal O}(K^{8/9})$ regret and greatly improves over the best existing bound $\tilde{\mathcal O}(K^{14/15})$. This algorithm relies on a better alternative to the Matrix Geometric Resampling procedure by Neu & Olkhovskaya (2020), which could again be of independent interest.

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NeurIPS Conference 2023 Conference Paper

Uncoupled and Convergent Learning in Two-Player Zero-Sum Markov Games with Bandit Feedback

  • Yang Cai
  • Haipeng Luo
  • Chen-Yu Wei
  • Weiqiang Zheng

We revisit the problem of learning in two-player zero-sum Markov games, focusing on developing an algorithm that is *uncoupled*, *convergent*, and *rational*, with non-asymptotic convergence rates to Nash equilibrium. We start from the case of stateless matrix game with bandit feedback as a warm-up, showing an $\tilde{\mathcal{O}}(t^{-\frac{1}{8}})$ last-iterate convergence rate. To the best of our knowledge, this is the first result that obtains finite last-iterate convergence rate given access to only bandit feedback. We extend our result to the case of irreducible Markov games, providing a last-iterate convergence rate of $\tilde{\mathcal{O}}(t^{-\frac{1}{9+\varepsilon}})$ for any $\varepsilon>0$. Finally, we study Markov games without any assumptions on the dynamics, and show a *path convergence* rate, a new notion of convergence we defined, of $\tilde{\mathcal{O}}(t^{-\frac{1}{10}})$. Our algorithm removes the synchronization and prior knowledge requirement of Wei et al. (2021), which pursued the same goals as us for irreducible Markov games. Our algorithm is related to Chen et al. (2021) and Cen et al. (2021)'s and also builds on the entropy regularization technique. However, we remove their requirement of communications on the entropy values, making our algorithm entirely uncoupled.

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ICML Conference 2022 Conference Paper

Independent Policy Gradient for Large-Scale Markov Potential Games: Sharper Rates, Function Approximation, and Game-Agnostic Convergence

  • Dongsheng Ding
  • Chen-Yu Wei
  • Kaiqing Zhang
  • Mihailo R. Jovanovic

We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPGs). To learn a Nash equilibrium of an MPG in which the size of state space and/or the number of players can be very large, we propose new independent policy gradient algorithms that are run by all players in tandem. When there is no uncertainty in the gradient evaluation, we show that our algorithm finds an $\epsilon$-Nash equilibrium with $O(1/\epsilon^2)$ iteration complexity which does not explicitly depend on the state space size. When the exact gradient is not available, we establish $O(1/\epsilon^5)$ sample complexity bound in a potentially infinitely large state space for a sample-based algorithm that utilizes function approximation. Moreover, we identify a class of independent policy gradient algorithms that enjoy convergence for both zero-sum Markov games and Markov cooperative games with the players that are oblivious to the types of games being played. Finally, we provide computational experiments to corroborate the merits and the effectiveness of our theoretical developments.

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ICML Conference 2022 Conference Paper

Personalization Improves Privacy-Accuracy Tradeoffs in Federated Learning

  • Alberto Bietti
  • Chen-Yu Wei
  • Miroslav Dudík
  • John Langford 0001
  • Zhiwei Steven Wu

Large-scale machine learning systems often involve data distributed across a collection of users. Federated learning algorithms leverage this structure by communicating model updates to a central server, rather than entire datasets. In this paper, we study stochastic optimization algorithms for a personalized federated learning setting involving local and global models subject to user-level (joint) differential privacy. While learning a private global model induces a cost of privacy, local learning is perfectly private. We provide generalization guarantees showing that coordinating local learning with private centralized learning yields a generically useful and improved tradeoff between accuracy and privacy. We illustrate our theoretical results with experiments on synthetic and real-world datasets.

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ICML Conference 2021 Conference Paper

Achieving Near Instance-Optimality and Minimax-Optimality in Stochastic and Adversarial Linear Bandits Simultaneously

  • Chung-Wei Lee
  • Haipeng Luo
  • Chen-Yu Wei
  • Mengxiao Zhang
  • Xiaojin Zhang 0002

In this work, we develop linear bandit algorithms that automatically adapt to different environments. By plugging a novel loss estimator into the optimization problem that characterizes the instance-optimal strategy, our first algorithm not only achieves nearly instance-optimal regret in stochastic environments, but also works in corrupted environments with additional regret being the amount of corruption, while the state-of-the-art (Li et al. , 2019) achieves neither instance-optimality nor the optimal dependence on the corruption amount. Moreover, by equipping this algorithm with an adversarial component and carefully-designed testings, our second algorithm additionally enjoys minimax-optimal regret in completely adversarial environments, which is the first of this kind to our knowledge. Finally, all our guarantees hold with high probability, while existing instance-optimal guarantees only hold in expectation.

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ICLR Conference 2021 Conference Paper

Linear Last-iterate Convergence in Constrained Saddle-point Optimization

  • Chen-Yu Wei
  • Chung-Wei Lee
  • Mengxiao Zhang
  • Haipeng Luo

Optimistic Gradient Descent Ascent (OGDA) and Optimistic Multiplicative Weights Update (OMWU) for saddle-point optimization have received growing attention due to their favorable last-iterate convergence. However, their behaviors for simple bilinear games over the probability simplex are still not fully understood --- previous analysis lacks explicit convergence rates, only applies to an exponentially small learning rate, or requires additional assumptions such as the uniqueness of the optimal solution. In this work, we significantly expand the understanding of last-iterate convergence for OGDA and OMWU in the constrained setting. Specifically, for OMWU in bilinear games over the simplex, we show that when the equilibrium is unique, linear last-iterate convergence is achievable with a constant learning rate, which improves the result of (Daskalakis & Panageas, 2019) under the same assumption. We then significantly extend the results to more general objectives and feasible sets for the projected OGDA algorithm, by introducing a sufficient condition under which OGDA exhibits concrete last-iterate convergence rates with a constant learning rate. We show that bilinear games over any polytope satisfy this condition and OGDA converges exponentially fast even without the unique equilibrium assumption. Our condition also holds for strongly-convex-strongly-concave functions, recovering the result of (Hsieh et al., 2019). Finally, we provide experimental results to further support our theory.

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NeurIPS Conference 2021 Conference Paper

Policy Optimization in Adversarial MDPs: Improved Exploration via Dilated Bonuses

  • Haipeng Luo
  • Chen-Yu Wei
  • Chung-Wei Lee

Policy optimization is a widely-used method in reinforcement learning. Due to its local-search nature, however, theoretical guarantees on global optimality often rely on extra assumptions on the Markov Decision Processes (MDPs) that bypass the challenge of global exploration. To eliminate the need of such assumptions, in this work, we develop a general solution that adds dilated bonuses to the policy update to facilitate global exploration. To showcase the power and generality of this technique, we apply it to several episodic MDP settings with adversarial losses and bandit feedback, improving and generalizing the state-of-the-art. Specifically, in the tabular case, we obtain $\widetilde{\mathcal{O}}(\sqrt{T})$ regret where $T$ is the number of episodes, improving the $\widetilde{\mathcal{O}}({T}^{\frac{2}{3}})$ regret bound by Shani et al. [2020]. When the number of states is infinite, under the assumption that the state-action values are linear in some low-dimensional features, we obtain $\widetilde{\mathcal{O}}({T}^{\frac{2}{3}})$ regret with the help of a simulator, matching the result of Neu and Olkhovskaya [2020] while importantly removing the need of an exploratory policy that their algorithm requires. To our knowledge, this is the first algorithm with sublinear regret for linear function approximation with adversarial losses, bandit feedback, and no exploratory assumptions. Finally, we also discuss how to further improve the regret or remove the need of a simulator using dilated bonuses, when an exploratory policy is available.

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NeurIPS Conference 2020 Conference Paper

Bias no more: high-probability data-dependent regret bounds for adversarial bandits and MDPs

  • Chung-Wei Lee
  • Haipeng Luo
  • Chen-Yu Wei
  • Mengxiao Zhang

We develop a new approach to obtaining high probability regret bounds for online learning with bandit feedback against an adaptive adversary. While existing approaches all require carefully constructing optimistic and biased loss estimators, our approach uses standard unbiased estimators and relies on a simple increasing learning rate schedule, together with the help of logarithmically homogeneous self-concordant barriers and a strengthened Freedman's inequality. Besides its simplicity, our approach enjoys several advantages. First, the obtained high-probability regret bounds are data-dependent and could be much smaller than the worst-case bounds, which resolves an open problem asked by Neu (2015). Second, resolving another open problem of Bartlett et al. (2008) and Abernethy and Rakhlin (2009), our approach leads to the first general and efficient algorithm with a high-probability regret bound for adversarial linear bandits, while previous methods are either inefficient or only applicable to specific action sets. Finally, our approach can also be applied to learning adversarial Markov Decision Processes and provides the first algorithm with a high-probability small-loss bound for this problem.

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ICML Conference 2020 Conference Paper

Model-free Reinforcement Learning in Infinite-horizon Average-reward Markov Decision Processes

  • Chen-Yu Wei
  • Mehdi Jafarnia-Jahromi
  • Haipeng Luo
  • Hiteshi Sharma
  • Rahul Jain 0002

Model-free reinforcement learning is known to be memory and computation efficient and more amendable to large scale problems. In this paper, two model-free algorithms are introduced for learning infinite-horizon average-reward Markov Decision Processes (MDPs). The first algorithm reduces the problem to the discounted-reward version and achieves $\mathcal{O}(T^{2/3})$ regret after $T$ steps, under the minimal assumption of weakly communicating MDPs. To our knowledge, this is the first model-free algorithm for general MDPs in this setting. The second algorithm makes use of recent advances in adaptive algorithms for adversarial multi-armed bandits and improves the regret to $\mathcal{O}(\sqrt{T})$, albeit with a stronger ergodic assumption. This result significantly improves over the $\mathcal{O}(T^{3/4})$ regret achieved by the only existing model-free algorithm by Abbasi-Yadkori et al. (2019) for ergodic MDPs in the infinite-horizon average-reward setting.

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ICML Conference 2019 Conference Paper

Bandit Multiclass Linear Classification: Efficient Algorithms for the Separable Case

  • Alina Beygelzimer
  • Dávid Pál
  • Balázs Szörényi
  • Devanathan Thiruvenkatachari
  • Chen-Yu Wei
  • Chicheng Zhang

We study the problem of efficient online multiclass linear classification with bandit feedback, where all examples belong to one of $K$ classes and lie in the $d$-dimensional Euclidean space. Previous works have left open the challenge of designing efficient algorithms with finite mistake bounds when the data is linearly separable by a margin $\gamma$. In this work, we take a first step towards this problem. We consider two notions of linear separability: strong and weak. 1. Under the strong linear separability condition, we design an efficient algorithm that achieves a near-optimal mistake bound of $O\left(\frac{K}{\gamma^2} \right)$. 2. Under the more challenging weak linear separability condition, we design an efficient algorithm with a mistake bound of $2^{\widetilde{O}(\min(K \log^2 \frac{1}{\gamma}, \sqrt{\frac{1}{\gamma}} \log K))}$. Our algorithm is based on kernel Perceptron, which is inspired by the work of Klivans & Servedio (2008) on improperly learning intersection of halfspaces.

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ICML Conference 2019 Conference Paper

Beating Stochastic and Adversarial Semi-bandits Optimally and Simultaneously

  • Julian Zimmert
  • Haipeng Luo
  • Chen-Yu Wei

We develop the first general semi-bandit algorithm that simultaneously achieves $\mathcal{O}(\log T)$ regret for stochastic environments and $\mathcal{O}(\sqrt{T})$ regret for adversarial environments without knowledge of the regime or the number of rounds $T$. The leading problem-dependent constants of our bounds are not only optimal in some worst-case sense studied previously, but also optimal for two concrete instances of semi-bandit problems. Our algorithm and analysis extend the recent work of (Zimmert & Seldin, 2019) for the special case of multi-armed bandits, but importantly requires a novel hybrid regularizer designed specifically for semi-bandit. Experimental results on synthetic data show that our algorithm indeed performs well uniformly over different environments. We finally provide a preliminary extension of our results to the full bandit feedback.

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NeurIPS Conference 2018 Conference Paper

Efficient Online Portfolio with Logarithmic Regret

  • Haipeng Luo
  • Chen-Yu Wei
  • Kai Zheng

We study the decades-old problem of online portfolio management and propose the first algorithm with logarithmic regret that is not based on Cover's Universal Portfolio algorithm and admits much faster implementation. Specifically Universal Portfolio enjoys optimal regret $\mathcal{O}(N\ln T)$ for $N$ financial instruments over $T$ rounds, but requires log-concave sampling and has a large polynomial running time. Our algorithm, on the other hand, ensures a slightly larger but still logarithmic regret of $\mathcal{O}(N^2(\ln T)^4)$, and is based on the well-studied Online Mirror Descent framework with a novel regularizer that can be implemented via standard optimization methods in time $\mathcal{O}(TN^{2. 5})$ per round. The regret of all other existing works is either polynomial in $T$ or has a potentially unbounded factor such as the inverse of the smallest price relative.

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NeurIPS Conference 2017 Conference Paper

Online Reinforcement Learning in Stochastic Games

  • Chen-Yu Wei
  • Yi-Te Hong
  • Chi-Jen Lu

We study online reinforcement learning in average-reward stochastic games (SGs). An SG models a two-player zero-sum game in a Markov environment, where state transitions and one-step payoffs are determined simultaneously by a learner and an adversary. We propose the \textsc{UCSG} algorithm that achieves a sublinear regret compared to the game value when competing with an arbitrary opponent. This result improves previous ones under the same setting. The regret bound has a dependency on the \textit{diameter}, which is an intrinsic value related to the mixing property of SGs. Slightly extended, \textsc{UCSG} finds an $\varepsilon$-maximin stationary policy with a sample complexity of $\tilde{\mathcal{O}}\left(\text{poly}(1/\varepsilon)\right)$, where $\varepsilon$ is the error parameter. To the best of our knowledge, this extended result is the first in the average-reward setting. In the analysis, we develop Markov chain's perturbation bounds for mean first passage times and techniques to deal with non-stationary opponents, which may be of interest in their own right.

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NeurIPS Conference 2016 Conference Paper

Tracking the Best Expert in Non-stationary Stochastic Environments

  • Chen-Yu Wei
  • Yi-Te Hong
  • Chi-Jen Lu

We study the dynamic regret of multi-armed bandit and experts problem in non-stationary stochastic environments. We introduce a new parameter $\W$, which measures the total statistical variance of the loss distributions over $T$ rounds of the process, and study how this amount affects the regret. We investigate the interaction between $\W$ and $\Gamma$, which counts the number of times the distributions change, as well as $\W$ and $V$, which measures how far the distributions deviates over time. One striking result we find is that even when $\Gamma$, $V$, and $\Lambda$ are all restricted to constant, the regret lower bound in the bandit setting still grows with $T$. The other highlight is that in the full-information setting, a constant regret becomes achievable with constant $\Gamma$ and $\Lambda$, as it can be made independent of $T$, while with constant $V$ and $\Lambda$, the regret still has a $T^{1/3}$ dependency. We not only propose algorithms with upper bound guarantee, but prove their matching lower bounds as well.

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