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arXiv · 2406.01234

Achieving Tractable Minimax Optimal Regret in Average Reward MDPs

Victor Boone·Zihan Zhang
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Abstract

In recent years, significant attention has been directed towards learning average-reward Markov Decision Processes (MDPs). However, existing algorithms either suffer from sub-optimal regret guarantees or computational inefficiencies. In this paper, we present the first tractable algorithm with minimax optimal regret of $\widetilde{\mathrm{O}}(\sqrt{\mathrm{sp}(h^*) S A T})$, where $\mathrm{sp}(h^*)$ is the span of the optimal bias function $h^*$, $S \times A$ is the size of the state-action space and $T$ the number of learning steps. Remarkably, our algorithm does not require prior information on $\mathrm{sp}(h^*)$. Our algorithm relies on a novel subroutine, Projected Mitigated Extended Value Iteration (PMEVI), to compute bias-constrained optimal policies efficiently. This subroutine can be applied to various previous algorithms to improve regret bounds.

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Victor Boone, Zihan Zhang. 2024-06-03. Achieving Tractable Minimax Optimal Regret in Average Reward MDPs. https://arxiv.org/abs/2406.01234

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