Related papers: Optimal Sample Complexity for Average Reward Markov Decision Processes

Optimal Sample Complexity for Average Reward Markov Decision Processes

URL: http://arxiv.org/abs/2310.08833v2
Date: Mon, 12 Feb 2024 19:06:53 GMT
Title: Optimal Sample Complexity for Average Reward Markov Decision Processes
Authors: Shengbo Wang, Jose Blanchet, and Peter Glynn
Abstract summary: We develop an estimator for the optimal policy of average reward MDPs with a sample complexity of $widetilde O(|S||A|t_textmix2 epsilon-2)$. This marks the first algorithm and analysis to reach the literature's lower bound.
Score: 1.0445957451908694
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We resolve the open question regarding the sample complexity of policy learning for maximizing the long-run average reward associated with a uniformly ergodic Markov decision process (MDP), assuming a generative model. In this context, the existing literature provides a sample complexity upper bound of $\widetilde O(|S||A|t_{\text{mix}}^2 \epsilon^{-2})$ and a lower bound of $\Omega(|S||A|t_{\text{mix}} \epsilon^{-2})$. In these expressions, $|S|$ and $|A|$ denote the cardinalities of the state and action spaces respectively, $t_{\text{mix}}$ serves as a uniform upper limit for the total variation mixing times, and $\epsilon$ signifies the error tolerance. Therefore, a notable gap of $t_{\text{mix}}$ still remains to be bridged. Our primary contribution is the development of an estimator for the optimal policy of average reward MDPs with a sample complexity of $\widetilde O(|S||A|t_{\text{mix}}\epsilon^{-2})$. This marks the first algorithm and analysis to reach the literature's lower bound. Our new algorithm draws inspiration from ideas in Li et al. (2020), Jin and Sidford (2021), and Wang et al. (2023). Additionally, we conduct numerical experiments to validate our theoretical findings.

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