Episodic Reinforcement Learning in Finite MDPs: Minimax Lower Bounds Revisited

• URL: http://arxiv.org/abs/2010.03531v1
• Date: Wed, 7 Oct 2020 17:23:01 GMT
• Title: Episodic Reinforcement Learning in Finite MDPs: Minimax Lower Bounds Revisited
• Authors: Omar Darwiche Domingues, Pierre M\'enard, Emilie Kaufmann, Michal Valko
• Abstract summary: We propose new problem-independent lower bounds on the sample complexity and regret in episodic MDPs. Our main contribution is a novel lower bound of $Omega((H3SA/epsilon2)log (1/delta))$ on the sample complexity of an $(varepsilon,delta)$-PAC algorithm for best policy identification in a non-stationary MDP.
• Score: 46.682733513730334
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose new problem-independent lower bounds on the sample complexity and regret in episodic MDPs, with a particular focus on the non-stationary case in which the transition kernel is allowed to change in each stage of the episode. Our main contribution is a novel lower bound of $\Omega((H^3SA/\epsilon^2)\log(1/\delta))$ on the sample complexity of an $(\varepsilon,\delta)$-PAC algorithm for best policy identification in a non-stationary MDP. This lower bound relies on a construction of "hard MDPs" which is different from the ones previously used in the literature. Using this same class of MDPs, we also provide a rigorous proof of the $\Omega(\sqrt{H^3SAT})$ regret bound for non-stationary MDPs. Finally, we discuss connections to PAC-MDP lower bounds.

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