Timezone: »

Breaking the Sample Complexity Barrier to Regret-Optimal Model-Free Reinforcement Learning
Gen Li · Laixi Shi · Yuxin Chen · Yuantao Gu · Yuejie Chi

Wed Dec 08 04:30 PM -- 06:00 PM (PST) @ None #None
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. 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.

Author Information

Gen Li (Tsinghua University)
Laixi Shi (Carnegie Mellon University)

I'm actively looking for a research internship in Summer 2022. My research interests include signal processing, nonconvex optimization, high-dimensional statistical estimation, and reinforcement learning, ranging from theory to application.

Yuxin Chen (Princeton University)
Yuantao Gu (Tsinghua University)
Yuejie Chi (Carnegie Mellon University)

Related Events (a corresponding poster, oral, or spotlight)

More from the Same Authors