Variance-Reduced Cascade Q-learning: Algorithms and Sample Complexity

• URL: http://arxiv.org/abs/2408.06544v1
• Date: Tue, 13 Aug 2024 00:34:33 GMT
• Title: Variance-Reduced Cascade Q-learning: Algorithms and Sample Complexity
• Authors: Mohammad Boveiri, Peyman Mohajerin Esfahani,
• Abstract summary: We introduce and analyze a novel model-free algorithm called Variance-Reduced Cascade Q-learning (VRCQ) VRCQ provides superior guarantees in the $ell_infty$-norm compared with the existing model-free approximation-type algorithms.
• Score: 3.4376560669160394
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of estimating the optimal Q-function of $\gamma$-discounted Markov decision processes (MDPs) under the synchronous setting, where independent samples for all state-action pairs are drawn from a generative model at each iteration. We introduce and analyze a novel model-free algorithm called Variance-Reduced Cascade Q-learning (VRCQ). VRCQ comprises two key building blocks: (i) the established direct variance reduction technique and (ii) our proposed variance reduction scheme, Cascade Q-learning. By leveraging these techniques, VRCQ provides superior guarantees in the $\ell_\infty$-norm compared with the existing model-free stochastic approximation-type algorithms. Specifically, we demonstrate that VRCQ is minimax optimal. Additionally, when the action set is a singleton (so that the Q-learning problem reduces to policy evaluation), it achieves non-asymptotic instance optimality while requiring the minimum number of samples theoretically possible. Our theoretical results and their practical implications are supported by numerical experiments.

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