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# Is Reinforcement Learning More Difficult Than Bandits? A Near-optimal Algorithm Escaping the Curse of Horizon

*Proceedings of Thirty Fourth Conference on Learning Theory*, PMLR 134:4528-4531, 2021.

#### Abstract

Episodic reinforcement learning and contextual bandits are two widely studied sequential decision-making problems. Episodic reinforcement learning generalizes contextual bandits and is often perceived to be more difficult due to long planning horizon and unknown state-dependent transitions. The current paper shows that the long planning horizon and the unknown state-dependent transitions (at most) pose little additional difficulty on sample complexity. We consider the episodic reinforcement learning with S states, A actions, planning horizon H, total reward bounded by 1, and the agent plays for K episodes. We propose a new algorithm, Monotonic Value Propagation (MVP), which relies on a new Bernstein-type bonus. The new bonus only requires tweaking the constants to ensure optimism and thus is significantly simpler than existing bonus constructions. We show MVP enjoys an $O\left(\left(\sqrt{SAK} + S^2A\right) \poly\log \left(SAHK\right)\right)$ regret, approaching the $\Omega\left(\sqrt{SAK}\right)$ lower bound of contextual bandits. Notably, this result 1) exponentially improves the state-of-the-art polynomial-time algorithms by Dann et al. [2019], Zanette et al. [2019], and Zhang et al. [2020] in terms of the dependency on H, and 2) exponentially improves the running time in [Wang et al. 2020] and significantly improves the dependency on S, A and K in sample complexity.