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

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. Compared to existing bonus constructions, the new bonus is tighter since it is based on a well-designed monotonic value function. In particular, the constants in the bonus should be subtly setting to ensure optimism and monotonicity. We show MVP enjoys an Oleft(left(√SAK + S2Aright) polylog left(SAHKright)right) regret, approaching the Omegaleft(√SAKright) lower bound of contextual bandits up to logarithmic terms. Notably, this result 1) exponentially improves the state-of-the-art polynomial-time algorithms by Dann et al. [2019] and Zanette et al. [2019] 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.