Almost Sure Convergence Rates and Concentration of Stochastic Approximation and Reinforcement Learning with Markovian Noise

• URL: http://arxiv.org/abs/2411.13711v1
• Date: Wed, 20 Nov 2024 21:09:09 GMT
• Title: Almost Sure Convergence Rates and Concentration of Stochastic Approximation and Reinforcement Learning with Markovian Noise
• Authors: Xiaochi Qian, Zixuan Xie, Xinyu Liu, Shangtong Zhang,
• Abstract summary: We provide the first almost sure convergence rate for $Q$-learning with Markovian samples without count-based learning rates. We also provide the first concentration bound for off-policy temporal difference learning with Markovian samples.
• Score: 31.241889735283166
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• Abstract: This paper establishes the first almost sure convergence rate and the first maximal concentration bound with exponential tails for general contractive stochastic approximation algorithms with Markovian noise. As a corollary, we also obtain convergence rates in $L^p$. Key to our successes is a novel discretization of the mean ODE of stochastic approximation algorithms using intervals with diminishing (instead of constant) length. As applications, we provide the first almost sure convergence rate for $Q$-learning with Markovian samples without count-based learning rates. We also provide the first concentration bound for off-policy temporal difference learning with Markovian samples.

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