Episodic Reinforcement Learning in Finite MDPs: Minimax Lower Bounds Revisited
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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 Ω((H^3SA/ϵ^2)log(1/δ)) on the sample complexity of an (ε,δ)-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 Ω(√(H^3SAT)) regret bound for non-stationary MDPs. Finally, we discuss connections to PAC-MDP lower bounds.
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