For average-reward MDPs with total-variation uncertainty, the minimax sample complexity is SA/epsilon^2 times min{H0,Hsigma}, with an extra SA sigma Hsigma^2/epsilon^2 term in the low-tolerance regime, and the paper provides matching algorithms.
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Robust Average-Reward Markov Decision Processes: Minimax-Optimal Learning via Plug-in Reductions
For average-reward MDPs with total-variation uncertainty, the minimax sample complexity is SA/epsilon^2 times min{H0,Hsigma}, with an extra SA sigma Hsigma^2/epsilon^2 term in the low-tolerance regime, and the paper provides matching algorithms.