Beyond Value-Function Gaps: Improved Instance-Dependent Regret Bounds for Episodic Reinforcement LearningDownload PDF

21 May 2021, 20:47 (edited 26 Oct 2021)NeurIPS 2021 SpotlightReaders: Everyone
  • Keywords: reinforcement learning, MDP, rl, instance-dependent regret bounds, theory, regret, gap-dependent
  • TL;DR: We provide improved gap-dependent regret bounds for reinforcement learning in finite episodic Markov decision processes.
  • Abstract: We provide improved gap-dependent regret bounds for reinforcement learning in finite episodic Markov decision processes. Compared to prior work, our bounds depend on alternative definitions of gaps. These definitions are based on the insight that, in order to achieve a favorable regret, an algorithm does not need to learn how to behave optimally in states that are not reached by an optimal policy. We prove tighter upper regret bounds for optimistic algorithms and accompany them with new information-theoretic lower bounds for a large class of MDPs. Our results show that optimistic algorithms can not achieve the information-theoretic lower bounds even in deterministic MDPs unless there is a unique optimal policy.
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