Convergence and Sample Complexity of First-Order Methods for Agnostic Reinforcement Learning

• URL: http://arxiv.org/abs/2507.04406v1
• Date: Sun, 06 Jul 2025 14:40:05 GMT
• Title: Convergence and Sample Complexity of First-Order Methods for Agnostic Reinforcement Learning
• Authors: Uri Sherman, Tomer Koren, Yishay Mansour,
• Abstract summary: We study reinforcement learning in the policy learning setting.<n>The goal is to find a policy whose performance is competitive with the best policy in a given class of interest.
• Score: 66.4260157478436
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study reinforcement learning (RL) in the agnostic policy learning setting, where the goal is to find a policy whose performance is competitive with the best policy in a given class of interest $\Pi$ -- crucially, without assuming that $\Pi$ contains the optimal policy. We propose a general policy learning framework that reduces this problem to first-order optimization in a non-Euclidean space, leading to new algorithms as well as shedding light on the convergence properties of existing ones. Specifically, under the assumption that $\Pi$ is convex and satisfies a variational gradient dominance (VGD) condition -- an assumption known to be strictly weaker than more standard completeness and coverability conditions -- we obtain sample complexity upper bounds for three policy learning algorithms: \emph{(i)} Steepest Descent Policy Optimization, derived from a constrained steepest descent method for non-convex optimization; \emph{(ii)} the classical Conservative Policy Iteration algorithm \citep{kakade2002approximately} reinterpreted through the lens of the Frank-Wolfe method, which leads to improved convergence results; and \emph{(iii)} an on-policy instantiation of the well-studied Policy Mirror Descent algorithm. Finally, we empirically evaluate the VGD condition across several standard environments, demonstrating the practical relevance of our key assumption.

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