Breaking the Sample Complexity Barrier to Regret-Optimal Model-Free Reinforcement Learning
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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 √(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 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 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 reference-advantage decomposition), the proposed algorithm employs an early-settled reference update rule, with the aid of two Q-learning sequences with upper and lower confidence bounds. The design principle of our early-settled variance reduction method might be of independent interest to other RL settings that involve intricate exploration-exploitation trade-offs.
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