Distributionally Robust Average-Reward Reinforcement Learning: Finite-Sample Guarantees under Weak Communication

arXiv:2609.32727v1 Announce Type: new Abstract: We study distributionally robust reinforcement learning (DR-RL) in the average-reward setting under weak communication. Our main result provides finite-sample guarantees for estimating the robust optimal average reward and learning a near-optimal policy, covering both SA-rectangular and S-rectangular structures with divergence-based and distance-based uncertainty sets. Specifically, for Kullback--Leibler and f_k-divergence balls, we establish explicit radius conditions under which the robust average-reward Bellman equation admits a constant-gain solution, while for total variation and Wasserstein balls, any positive radius suffices without requiring the nominal MDP to be weakly communicating. Our algorithm is prior-knowledge-free and achieves sample complexities of widetilde O(|S||A|p_{wedge}^{-1}operatorname{Span}^{2}(u_{elta}^{ast})epsilon^{-2}) for estimating the robust optimal average reward and widetilde O(|S||A|p_{wedge}^{-2}operatorname{Span}^{2}(u_{elta}^{ast})epsilon^{-2}) for learning an epsilon-optimal policy. Here, p_{wedge} is the smallest positive nominal transition probability and u_{elta}^{ast} is a robust optimal bias function. We further provide an almost-tight explicit upper bound on operatorname{Span}(u_{elta}^{ast}). Finally, we validate the predicted n^{-1/2} convergence rate through numerical experiments.

Source: arXiv cs.LG | 2026-09-29