Achieving Tractable Minimax Optimal Regret in Average Reward MDPs

• URL: http://arxiv.org/abs/2406.01234v1
• Date: Mon, 3 Jun 2024 11:53:44 GMT
• Title: Achieving Tractable Minimax Optimal Regret in Average Reward MDPs
• Authors: Victor Boone, Zihan Zhang,
• Abstract summary: We present the first tractable algorithm with minimax optimal regret of $widetildemathrmO(sqrtmathrmsp(h*) S A T)$. Remarkably, our algorithm does not require prior information on $mathrmsp(h*)$.
• Score: 19.663336027878408
• License: http://creativecommons.org/licenses/by/4.0/
• 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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