Sample Complexity of Distributionally Robust Average-Reward Reinforcement Learning

• URL: http://arxiv.org/abs/2505.10007v1
• Date: Thu, 15 May 2025 06:42:25 GMT
• Title: Sample Complexity of Distributionally Robust Average-Reward Reinforcement Learning
• Authors: Zijun Chen, Shengbo Wang, Nian Si,
• Abstract summary: We propose two algorithms that achieve near-optimal sample complexity.<n>We prove that both algorithms attain a sample complexity of $widetildeOleft(|mathbfS||mathbfA| t_mathrmmix2varepsilon-2right)$ for estimating the optimal policy.<n>This represents the first finite-sample convergence guarantee for DR average-reward reinforcement learning.
• Score: 5.8191965840377735
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Motivated by practical applications where stable long-term performance is critical-such as robotics, operations research, and healthcare-we study the problem of distributionally robust (DR) average-reward reinforcement learning. We propose two algorithms that achieve near-optimal sample complexity. The first reduces the problem to a DR discounted Markov decision process (MDP), while the second, Anchored DR Average-Reward MDP, introduces an anchoring state to stabilize the controlled transition kernels within the uncertainty set. Assuming the nominal MDP is uniformly ergodic, we prove that both algorithms attain a sample complexity of $\widetilde{O}\left(|\mathbf{S}||\mathbf{A}| t_{\mathrm{mix}}^2\varepsilon^{-2}\right)$ for estimating the optimal policy as well as the robust average reward under KL and $f_k$-divergence-based uncertainty sets, provided the uncertainty radius is sufficiently small. Here, $\varepsilon$ is the target accuracy, $|\mathbf{S}|$ and $|\mathbf{A}|$ denote the sizes of the state and action spaces, and $t_{\mathrm{mix}}$ is the mixing time of the nominal MDP. This represents the first finite-sample convergence guarantee for DR average-reward reinforcement learning. We further validate the convergence rates of our algorithms through numerical experiments.

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