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arXiv · 2112.10935

Nearly Optimal Policy Optimization with Stable at Any Time Guarantee

Tianhao Wu·Yunchang Yang·Han Zhong·Liwei Wang·Simon S. Du·Jiantao Jiao
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Abstract

Policy optimization methods are one of the most widely used classes of Reinforcement Learning (RL) algorithms. However, theoretical understanding of these methods remains insufficient. Even in the episodic (time-inhomogeneous) tabular setting, the state-of-the-art theoretical result of policy-based method in \citet{shani2020optimistic} is only $\tilde{O}(\sqrt{S^2AH^4K})$ where $S$ is the number of states, $A$ is the number of actions, $H$ is the horizon, and $K$ is the number of episodes, and there is a $\sqrt{SH}$ gap compared with the information theoretic lower bound $\tilde{\Omega}(\sqrt{SAH^3K})$. To bridge such a gap, we propose a novel algorithm Reference-based Policy Optimization with Stable at Any Time guarantee (\algnameacro), which features the property "Stable at Any Time". We prove that our algorithm achieves $\tilde{O}(\sqrt{SAH^3K} + \sqrt{AH^4K})$ regret. When $S > H$, our algorithm is minimax optimal when ignoring logarithmic factors. To our best knowledge, RPO-SAT is the first computationally efficient, nearly minimax optimal policy-based algorithm for tabular RL.

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BibTeXRIS

Tianhao Wu, Yunchang Yang, Han Zhong, Liwei Wang, Simon S. Du, Jiantao Jiao. 2021-12-21. Nearly Optimal Policy Optimization with Stable at Any Time Guarantee. https://arxiv.org/abs/2112.10935

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