arXiv subjects

Chen-Yu Wei

Publications and source records attributed to Chen-Yu Wei.

At least 19 recordsLinked to original sources

arXiv2026

On the Complexity of Offline Reinforcement Learning with $Q^\star$-Approximation and Partial Coverage

We study offline reinforcement learning under $Q^\star$-approximation and partial coverage, a setting that motivates practical algorithms such as Conservative $Q$-Learning (CQL; Kumar et al., 2020) but has received limited theoretical attention. Our work is inspired by the following open question: "Are $Q^\star$-realizability and Bellman completeness sufficient for sample-efficient offline RL under partial coverage?" We answer in the negative via an information-theoretic lower bound. To identify additional structure that enables sample-efficient offline RL under partial coverage, we introduce a general decision-estimation framework, inspired by model-free decision-estimation coefficients (DEC) for online RL (Foster et al., 2023b; Liu et al., 2025b). Our framework decomposes offline RL complexity into decision complexity and value estimation error. This allows modular study of both sub-problems. Our result not only unifies existing results (Chen and Jiang, 2022; Uehara et al., 2023), but further improves and generalizes them. On the decision complexity side, our improvement includes: the first $\epsilon^{-2}$ sample complexity bound for soft $Q$-learning under partial coverage that improves Uehara et al.'s (2023) $\epsilon^{-4}$ bound, the removal of the need for additional online interaction in the value-gap setting of Chen and Jiang (2022), and new learnable settings beyond the above two cases. On the value estimation side, we provide a new characterization of the role of Bellman completeness under partial coverage, and the first characterization of offline learnability for general low-Bellman-rank MDPs (Jiang et al., 2017; Du et al., 2021; Jin et al., 2021). The latter is a canonical online RL setting that has remained unexplored in offline RL except for special cases. As a side contribution, our techniques give the first analysis of CQL in the function approximation setting.

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arXiv2026

Is Online Linear Optimization Sufficient for Strategic Robustness?

We consider bidding in repeated Bayesian first-price auctions. Bidding algorithms that achieve optimal regret have been extensively studied, but their strategic robustness to the seller's manipulation remains relatively underexplored. Bidding algorithms based on no-swap-regret algorithms achieve both desirable properties, but are suboptimal in terms of statistical and computational efficiency. In contrast, online gradient ascent is the only algorithm that achieves $O(\sqrt{TK})$ regret and strategic robustness [KSS24], where $T$ denotes the number of auctions and $K$ the number of bids. In this paper, we explore whether simple online linear optimization (OLO) algorithms suffice for bidding algorithms with both desirable properties. Our main result shows that sublinear linearized regret is sufficient for strategic robustness. Specifically, we construct simple black-box reductions that convert any OLO algorithm into a strategically robust no-regret bidding algorithm, in both known and unknown value distribution settings. For the known value distribution case, our reduction yields a bidding algorithm that achieves $O(\sqrt{T \log K})$ regret and strategic robustness (with exponential improvement on the $K$-dependence compared to [KSS24]). For the unknown value distribution case, our reduction gives a bidding algorithm with high-probability $O(\sqrt{T (\log K+\log(T/\delta)})$ regret and strategic robustness, while removing the bounded density assumption made in [KSS24].

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arXiv2026

Achieving Optimal Static and Dynamic Regret Simultaneously in Bandits with Deterministic Losses

In adversarial multi-armed bandits, two performance measures are commonly used: static regret, which compares the learner to the best fixed arm, and dynamic regret, which compares it to the best sequence of arms. While optimal algorithms are known for each measure individually, there is no known algorithm achieving optimal bounds for both simultaneously. Marinov and Zimmert [2021] first showed that such simultaneous optimality is impossible against an adaptive adversary. Our work takes a first step to demonstrate its possibility against an oblivious adversary when losses are deterministic. First, we extend the impossibility result of Marinov and Zimmert [2021] to the case of deterministic losses. Then, we present an algorithm achieving optimal static and dynamic regret simultaneously against an oblivious adversary. Together, they reveal a fundamental separation between adaptive and oblivious adversaries when multiple regret benchmarks are considered simultaneously. It also provides new insight into the long open problem of simultaneously achieving optimal regret against switching benchmarks of different numbers of switches. Our algorithm uses negative static regret to compensate for the exploration overhead incurred when controlling dynamic regret, and leverages Blackwell approachability to jointly control both regrets. This yields a new model selection procedure for bandits that may be of independent interest.

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arXiv2026

Save the Good Prefix: Precise Error Penalization via Process-Supervised RL to Enhance LLM Reasoning

Reinforcement learning (RL) has emerged as a powerful framework for improving the reasoning capabilities of large language models (LLMs). However, most existing RL approaches rely on sparse outcome rewards, which fail to credit correct intermediate steps in partially successful solutions. Process reward models (PRMs) offer fine-grained step-level supervision, but their scores are often noisy and difficult to evaluate. As a result, recent PRM benchmarks focus on a more objective capability: detecting the first incorrect step in a reasoning path. However, this evaluation target is misaligned with how PRMs are typically used in RL, where their step-wise scores are treated as raw rewards to maximize. To bridge this gap, we propose Verifiable Prefix Policy Optimization (VPPO), which uses PRMs only to localize the first error during RL. Given an incorrect rollout, VPPO partitions the trajectory into a verified correct prefix and an erroneous suffix based on the first error, rewarding the former while applying targeted penalties only after the detected mistake. This design yields stable, interpretable learning signals and improves credit assignment. Across multiple reasoning benchmarks, VPPO consistently outperforms sparse-reward RL and prior PRM-guided baselines on both Pass@1 and Pass@K.

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arXiv2025

Proximal Regret and Proximal Correlated Equilibria: A New Tractable Solution Concept for Online Learning and Games

Learning and computation of equilibria are central problems in game theory, theory of computation, and artificial intelligence. In this work, we introduce proximal regret, a new notion of regret based on proximal operators that lies strictly between external and swap regret. When every player employs a no-proximal-regret algorithm in a general convex game, the empirical distribution of play converges to proximal correlated equilibria (PCE), a refinement of coarse correlated equilibria. Our framework unifies several emerging notions in online learning and game theory-such as gradient equilibrium and semicoarse correlated equilibrium-and introduces new ones. Our main result shows that the classic Online Gradient Descent (GD) algorithm achieves an optimal $O(\sqrt{T})$ bound on proximal regret, revealing that GD, without modification, minimizes a stronger regret notion than external regret. This provides a new explanation for the empirically superior performance of gradient descent in online learning and games. We further extend our analysis to Mirror Descent in the Bregman setting and to Optimistic Gradient Descent, which yields faster convergence in smooth convex games.

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arXiv2025

An Improved Model-Free Decision-Estimation Coefficient with Applications in Adversarial MDPs

We study decision making with structured observation (DMSO). Previous work (Foster et al., 2021b, 2023a) has characterized the complexity of DMSO via the decision-estimation coefficient (DEC), but left a gap between the regret upper and lower bounds that scales with the size of the model class. To tighten this gap, Foster et al. (2023b) introduced optimistic DEC, achieving a bound that scales only with the size of the value-function class. However, their optimism-based exploration is only known to handle the stochastic setting, and it remains unclear whether it extends to the adversarial setting. We introduce Dig-DEC, a model-free DEC that removes optimism and drives exploration purely by information gain. Dig-DEC is always no larger than optimistic DEC and can be much smaller in special cases. Importantly, the removal of optimism allows it to handle adversarial environments without explicit reward estimators. By applying Dig-DEC to hybrid MDPs with stochastic transitions and adversarial rewards, we obtain the first model-free regret bounds for hybrid MDPs with bandit feedback under several general transition structures, resolving the main open problem left by Liu et al. (2025). We also improve the online function-estimation procedure in model-free learning: For average estimation error minimization, we refine the estimator in Foster et al. (2023b) to achieve sharper concentration, improving their regret bounds from $T^{3/4}$ to $T^{2/3}$ (on-policy) and from $T^{5/6}$ to $T^{7/9}$ (off-policy). For squared error minimization in Bellman-complete MDPs, we redesign their two-timescale procedure, improving the regret bound from $T^{2/3}$ to $\sqrt{T}$. This is the first time a DEC-based method achieves performance matching that of optimism-based approaches (Jin et al., 2021; Xie et al., 2023) in Bellman-complete MDPs.

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arXiv2025

An Improved Algorithm for Adversarial Linear Contextual Bandits via Reduction

We present an oracle-efficient, near-optimal algorithm for linear contextual bandits with adversarial losses and stochastic action sets, only requiring a linear optimization oracle for the action sets in each round. 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 $\widetilde{\mathcal{O}}(\min\{d^2\sqrt{T}, \sqrt{d^3T\log K}\})$ regret and runs in $\mathrm{poly}(d,T)$ time plus $\mathrm{poly}(d,T)$ calls to the linear optimization oracles, where $d$ is the feature dimension, $K$ 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, 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 $\widetilde{\mathcal{O}}(d\sqrt{L^\star})$, where $L^\star$ is the cumulative loss of the best policy.

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arXiv2025

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

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 $\widetilde{O}(d^{\frac{1}{5}} T^{-\frac{1}{5}})$ last-iterate convergence rate under bandit feedback, improving upon the previous best rates of $\widetilde{O}(\sqrt{d} T^{-\frac{1}{8}})$ and $\widetilde{O}(\sqrt{d} T^{-\frac{1}{6}})$.

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arXiv2025

Decision Making in Hybrid Environments: A Model Aggregation Approach

Recent work by Foster et al. (2021, 2022, 2023b) and Xu and Zeevi (2023) developed the framework of decision estimation coefficient (DEC) that characterizes the complexity of general online decision making problems and provides a general algorithm design principle. These works, however, either focus on the pure stochastic regime where the world remains fixed over time, or the pure adversarial regime where the world arbitrarily changes over time. For the hybrid regime where the dynamics of the world is fixed while the reward arbitrarily changes, they only give pessimistic bounds on the decision complexity. In this work, we propose a general extension of DEC that more precisely characterizes this case. Besides applications in special cases, our framework leads to a flexible algorithm design where the learner learns over subsets of the hypothesis set, trading estimation complexity with decision complexity, which could be of independent interest. Our work covers model-based learning and model-free learning in the hybrid regime, with a newly proposed extension of the bilinear classes (Du et al., 2021) to the adversarial-reward case. In addition, our method improves the best-known regret bounds for linear Q*/V* MDPs in the pure stochastic regime.

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arXiv2024

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

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 transition (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 function.

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arXiv2024

How Does Variance Shape the Regret in Contextual Bandits?

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 bounds, we show that the eluder dimension $d_\text{elu}$$-$a complexity measure of the function class$-$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 $d_{\text{elu}}\leq\sqrt{AT}$, 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 $\sqrt{d_\text{elu}\Lambda}+d_\text{elu}\leq\sqrt{AT}$. 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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arXiv2024

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

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 action chosen by the learner, and weak corruption, where the corruption level does not depend on the action chosen by the learner. 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 mis-specification, 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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arXiv2024

Near-Optimal Policy Optimization for Correlated Equilibrium in General-Sum Markov Games

We study policy optimization algorithms for computing correlated equilibria in multi-player general-sum Markov Games. Previous results achieve $O(T^{-1/2})$ convergence rate to a correlated equilibrium and an accelerated $O(T^{-3/4})$ convergence rate to the weaker notion of coarse correlated equilibrium. In this paper, we improve both results significantly by providing an uncoupled policy optimization algorithm that attains a near-optimal $\tilde{O}(T^{-1})$ convergence rate for computing a correlated equilibrium. Our algorithm is constructed by combining two main elements (i) smooth value updates and (ii) the optimistic-follow-the-regularized-leader algorithm with the log barrier regularizer.

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arXiv2024

Offline Reinforcement Learning: Role of State Aggregation and Trajectory Data

We revisit the problem of offline reinforcement learning with value function realizability but without Bellman completeness. Previous work by Xie and Jiang (2021) and Foster et al. (2022) left open the question whether a bounded concentrability coefficient along with trajectory-based offline data admits a polynomial sample complexity. In this work, we provide a negative answer to this question for the task of offline policy evaluation. In addition to addressing this question, we provide a rather complete picture for offline policy evaluation with only value function realizability. Our primary findings are threefold: 1) The sample complexity of offline policy evaluation is governed by the concentrability coefficient in an aggregated Markov Transition Model jointly determined by the function class and the offline data distribution, rather than that in the original MDP. This unifies and generalizes the ideas of Xie and Jiang (2021) and Foster et al. (2022), 2) The concentrability coefficient in the aggregated Markov Transition Model may grow exponentially with the horizon length, even when the concentrability coefficient in the original MDP is small and the offline data is admissible (i.e., the data distribution equals the occupancy measure of some policy), 3) Under value function realizability, there is a generic reduction that can convert any hard instance with admissible data to a hard instance with trajectory data, implying that trajectory data offers no extra benefits over admissible data. These three pieces jointly resolve the open problem, though each of them could be of independent interest.

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arXiv2024

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

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 [2003], which is guaranteed to exist for an arbitrary set of strategy modifications $\Phi$ even in non-concave games [Stolz and Lugosi, 2007]. 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 converges to the corresponding $\Phi$-equilibria. Additionally, we explore cases where $\Phi$ is infinite but consists of local modifications. We show that approximating local $\Phi$-equilibria beyond the first-order stationary regime is computationally intractable. In contrast, within this regime, we show Online Gradient Descent efficiently converges to $\Phi$-equilibria for several natural infinite families of modifications, including a new structural family of modifications inspired by the well-studied proximal operator.

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arXiv2024

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

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.

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arXiv2023

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

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. We start from the case of stateless matrix game with bandit feedback as a warm-up, showing an $O(t^{-\frac{1}{8}})$ 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 $O(t^{-\frac{1}{9+\varepsilon}})$ for any $\varepsilon>0$. Finally, we study Markov games without any assumptions on the dynamics, and show a path convergence rate, which is a new notion of convergence we defined, of $O(t^{-\frac{1}{10}})$. Our algorithm removes the coordination 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, Cen et al., 2021] 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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arXiv2023

No-Regret Online Reinforcement Learning with Adversarial Losses and Transitions

Existing online learning algorithms for adversarial Markov Decision Processes achieve ${O}(\sqrt{T})$ 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 $\widetilde{O}(\sqrt{T} + C^{\textsf{P}})$ regret where $C^{\textsf{P}}$ measures how adversarial the transition functions are and can be at most ${O}(T)$. While this algorithm itself requires knowledge of $C^{\textsf{P}}$, 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 $\widetilde{O}(U + \sqrt{UC^{\textsf{L}}} + C^{\textsf{P}})$ regret, where $U$ is some standard gap-dependent coefficient and $C^{\textsf{L}}$ is the amount of corruption on losses.

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