Distributionally Robust Average-Reward Reinforcement Learning: Finite-Sample Guarantees under Weak Communication
cs.LG, math.OC, stat.ML
Submitted: 2026-09-26
Updated: 2026-09-26
License: http://creativecommons.org/licenses/by/4.0/
The gist: We study distributionally robust reinforcement learning (DR-RL) in the average-reward setting under weak communication.
Terminology
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 O(S Ap-1 Span squared(u δ)ε-2) for estimating the robust optimal average reward and O(S Ap-2 Span squared(u δ)ε-2) for learning an ε-optimal policy. Here, p is the smallest positive nominal transition probability and u δ is a robust optimal bias function. We further provide an almost-tight explicit upper bound on Span(u δ). Finally, we validate the predicted n-1/2 convergence rate through numerical experiments.
Sources
- Learning Policy from a Single Trajectory in Average-Reward Markov Decision Process
- On Convergence of Average-Reward Q-Learning in Weakly Communicating Markov Decision Processes
- Bellman Optimality of Average-Reward Robust Markov Decision Processes with a Constant Gain
- Robust Average-Reward Markov Decision Processes: Minimax-Optimal Learning via Plug-in Reductions
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