Breaking the Sample Complexity Barrier to Regret-Optimal Model-Free Reinforcement Learning

Achieving sample efficiency in online episodic reinforcement learning (RL) requires optimally balancing exploration and exploitation. When it comes to a finite-horizon episodic Markov decision process with S states, A actions and horizon length H, substantial progress has been achieved towards characterizing the minimax-optimal regret, which scales on the order of \sqrt{H 2SAT} (modulo log factors) with T the total number of samples. While several competing solution paradigms have been proposed to minimize regret, they are either memory-inefficient, or fall short of optimality unless the sample size exceeds an enormous threshold (e.g., S 6A 4 \,\mathrm{poly}(H) for existing model-free methods).To overcome such a large sample size barrier to efficient RL, we design a novel model-free algorithm, with space complexity O(SAH), that achieves near-optimal regret as soon as the sample size exceeds the order of SA\,\mathrm{poly}(H) . In terms of this sample size requirement (also referred to the initial burn-in cost), our method improves --- by at least a factor of S 5A 3 --- upon any prior memory-efficient algorithm that is asymptotically regret-optimal. Leveraging the recently introduced variance reduction strategy (also called {\em reference-advantage decomposition}), the proposed algorithm employs an {\em early-settled} reference update rule, with the aid of two Q-learning sequences with upper and lower confidence bounds.