Optimistic Policy Optimization is Provably Efficient in Non-stationary MDPs

• URL: http://arxiv.org/abs/2110.08984v1
• Date: Mon, 18 Oct 2021 02:33:20 GMT
• Title: Optimistic Policy Optimization is Provably Efficient in Non-stationary MDPs
• Authors: Han Zhong, Zhuoran Yang, Zhaoran Wang Csaba Szepesv\'ari
• Abstract summary: We study episodic reinforcement learning (RL) in non-stationary linear kernel Markov decision processes (MDPs) We propose the $underlinetextp$eriodically $underlinetextr$estarted $underlinetexto$ptimistic $underlinetextp$olicy $underlinetexto$ptimization algorithm (PROPO)
• Score: 45.6318149525364
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study episodic reinforcement learning (RL) in non-stationary linear kernel Markov decision processes (MDPs). In this setting, both the reward function and the transition kernel are linear with respect to the given feature maps and are allowed to vary over time, as long as their respective parameter variations do not exceed certain variation budgets. We propose the $\underline{\text{p}}$eriodically $\underline{\text{r}}$estarted $\underline{\text{o}}$ptimistic $\underline{\text{p}}$olicy $\underline{\text{o}}$ptimization algorithm (PROPO), which is an optimistic policy optimization algorithm with linear function approximation. PROPO features two mechanisms: sliding-window-based policy evaluation and periodic-restart-based policy improvement, which are tailored for policy optimization in a non-stationary environment. In addition, only utilizing the technique of sliding window, we propose a value-iteration algorithm. We establish dynamic upper bounds for the proposed methods and a matching minimax lower bound which shows the (near-) optimality of the proposed methods. To our best knowledge, PROPO is the first provably efficient policy optimization algorithm that handles non-stationarity.

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