Horizon-Free Reinforcement Learning in Polynomial Time: the Power of Stationary Policies

• URL: http://arxiv.org/abs/2203.12922v1
• Date: Thu, 24 Mar 2022 08:14:12 GMT
• Title: Horizon-Free Reinforcement Learning in Polynomial Time: the Power of Stationary Policies
• Authors: Zihan Zhang, Xiangyang Ji, Simon S. Du
• Abstract summary: We design an algorithm that achieves an $Oleft(mathrmpoly(S,A,log K)sqrtKright)$ regret in contrast to existing bounds. Our result relies on a sequence of new structural lemmas establishing the approximation power, stability, and concentration property of stationary policies.
• Score: 88.75843804630772
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper gives the first polynomial-time algorithm for tabular Markov Decision Processes (MDP) that enjoys a regret bound \emph{independent on the planning horizon}. Specifically, we consider tabular MDP with $S$ states, $A$ actions, a planning horizon $H$, total reward bounded by $1$, and the agent plays for $K$ episodes. We design an algorithm that achieves an $O\left(\mathrm{poly}(S,A,\log K)\sqrt{K}\right)$ regret in contrast to existing bounds which either has an additional $\mathrm{polylog}(H)$ dependency~\citep{zhang2020reinforcement} or has an exponential dependency on $S$~\citep{li2021settling}. Our result relies on a sequence of new structural lemmas establishing the approximation power, stability, and concentration property of stationary policies, which can have applications in other problems related to Markov chains.

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