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arXiv 2203.12922cs.LG
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多项式时间中的无水平强化学习:稳态策略的力量

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

Tsinghua University(清华大学);University of Washington(华盛顿大学)

Zihan Zhang, Xiangyang Ji, Simon S. Du

摘要:

本文给出了表马尔可夫决策过程(MDP)的第一个具有后悔界\emph{independent on the planning horizon}的多项式时间算法。具体来说,我们考虑表格MDP与$S$状态,$A$行动,规划地平线$H$,总奖励由$1$界定,和代理播放$K$情节。我们设计了一个算法,实现了$O\left(\mathrm{poly}(S,A,\log K)\sqrt{K}\right)$遗憾,与现有的界限,要么有一个额外的$\mathrm{polylog}(H)$依赖性~ \citep{zhang2020reinforcement}或有一个指数依赖于$S$ ~ \citep{li2021settling}。我们的结果依赖于一系列新的结构引理建立的近似功率,稳定性和浓度属性的平稳政策,这可以在其他问题中的应用马尔可夫链。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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