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arXiv 1910.04077cs.LGcs.AIstat.ML
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利用状态-动作等价性的基于模型的强化学习

Model-Based Reinforcement Learning Exploiting State-Action Equivalence

Inria Lille – Nord Europe(法国国家信息与自动化研究所里尔-北欧中心)

Mahsa Asadi, Mohammad Sadegh Talebi, Hippolyte Bourel, Odalric-Ambrym Maillard

摘要:

利用马尔可夫决策过程(MDP)的状态空间中的等价属性已经在几项研究中进行了研究。本文研究了强化学习(RL)中的等价结构,其中不再假设转移分布是已知的。我们提出了一个概念之间的相似性的各种状态动作对的MDP的转移概率,它自然地定义了一个等价结构的状态动作空间。我们提出了等价感知的信心集的情况下,学习者知道的基础结构提前。这些集合可证明小于它们对应的等价遗忘的对应物。在更具有挑战性的情况下,一个未知的等价结构,我们提出了一种算法,称为近似等价,旨在找到一个(近似)等价结构,并定义置信集使用近似等价。为了说明所提出的置信集的有效性,我们提出了C-UCRL,作为一个自然的修改UCRL 2的RL在未贴现的MDP。在一个已知的等价结构的情况下,我们表明,C-UCRL改善了UCRL 2在遗憾方面的一个因素的$\sqrt{SA/C}$,在任何通信MDP与$S$状态,$A$行动,和$C$类,这对应于一个巨大的改善时,$C \ll SA$。据我们所知,这是第一个工作时,有效地利用MDP中的等价结构提供RL的遗憾界。在等价结构未知的情况下,我们通过数值实验表明,C-UCRL结合近似等价优于UCRL 2遍历MDP。

英文摘要:

Leveraging an equivalence property in the state-space of a Markov Decision Process (MDP) has been investigated in several studies. This paper studies equivalence structure in the reinforcement learning (RL) setup, where transition distributions are no longer assumed to be known. We present a notion of similarity between transition probabilities of various state-action pairs of an MDP, which naturally defines an equivalence structure in the state-action space. We present equivalence-aware confidence sets for the case where the learner knows the underlying structure in advance. These sets are provably smaller than their corresponding equivalence-oblivious counterparts. In the more challenging case of an unknown equivalence structure, we present an algorithm called ApproxEquivalence that seeks to find an (approximate) equivalence structure, and define confidence sets using the approximate equivalence. To illustrate the efficacy of the presented confidence sets, we present C-UCRL, as a natural modification of UCRL2 for RL in undiscounted MDPs. In the case of a known equivalence structure, we show that C-UCRL improves over UCRL2 in terms of regret by a factor of $\sqrt{SA/C}$, in any communicating MDP with $S$ states, $A$ actions, and $C$ classes, which corresponds to a massive improvement when $C \ll SA$. To the best of our knowledge, this is the first work providing regret bounds for RL when an equivalence structure in the MDP is efficiently exploited. In the case of an unknown equivalence structure, we show through numerical experiments that C-UCRL combined with ApproxEquivalence outperforms UCRL2 in ergodic MDPs.

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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