Finite-Time Error Bounds for Greedy-GQ

• URL: http://arxiv.org/abs/2209.02555v2
• Date: Thu, 2 May 2024 03:09:02 GMT
• Title: Finite-Time Error Bounds for Greedy-GQ
• Authors: Yue Wang, Yi Zhou, Shaofeng Zou,
• Abstract summary: We show that Greedy-GQ algorithm converges fast as finite-time error. Our analysis provides for faster convergence step-sizes for choosing step-sizes.
• Score: 20.51105692499517
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Greedy-GQ with linear function approximation, originally proposed in \cite{maei2010toward}, is a value-based off-policy algorithm for optimal control in reinforcement learning, and it has a non-linear two timescale structure with the non-convex objective function. This paper develops its tightest finite-time error bounds. We show that the Greedy-GQ algorithm converges as fast as $\mathcal{O}({1}/{\sqrt{T}})$ under the i.i.d.\ setting and $\mathcal{O}({\log T}/{\sqrt{T}})$ under the Markovian setting. We further design a variant of the vanilla Greedy-GQ algorithm using the nested-loop approach, and show that its sample complexity is $\mathcal{O}({\log(1/\epsilon)\epsilon^{-2}})$, which matches with the one of the vanilla Greedy-GQ. Our finite-time error bounds match with one of the stochastic gradient descent algorithms for general smooth non-convex optimization problems, despite its additonal challenge in the two time-scale updates. Our finite-sample analysis provides theoretical guidance on choosing step-sizes for faster convergence in practice, and suggests the trade-off between the convergence rate and the quality of the obtained policy. Our techniques provide a general approach for finite-sample analysis of non-convex two timescale value-based reinforcement learning algorithms.

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