Finite-Time Analysis for Double Q-learning

• URL: http://arxiv.org/abs/2009.14257v2
• Date: Mon, 12 Oct 2020 14:13:15 GMT
• Title: Finite-Time Analysis for Double Q-learning
• Authors: Huaqing Xiong, Lin Zhao, Yingbin Liang, Wei Zhang
• Abstract summary: We provide the first non-asymptotic, finite-time analysis for double Q-learning. We show that both synchronous and asynchronous double Q-learning are guaranteed to converge to an $epsilon$-accurate neighborhood of the global optimum.
• Score: 50.50058000948908
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Although Q-learning is one of the most successful algorithms for finding the best action-value function (and thus the optimal policy) in reinforcement learning, its implementation often suffers from large overestimation of Q-function values incurred by random sampling. The double Q-learning algorithm proposed in~\citet{hasselt2010double} overcomes such an overestimation issue by randomly switching the update between two Q-estimators, and has thus gained significant popularity in practice. However, the theoretical understanding of double Q-learning is rather limited. So far only the asymptotic convergence has been established, which does not characterize how fast the algorithm converges. In this paper, we provide the first non-asymptotic (i.e., finite-time) analysis for double Q-learning. We show that both synchronous and asynchronous double Q-learning are guaranteed to converge to an $\epsilon$-accurate neighborhood of the global optimum by taking $\tilde{\Omega}\left(\left( \frac{1}{(1-\gamma)^6\epsilon^2}\right)^{\frac{1}{\omega}} +\left(\frac{1}{1-\gamma}\right)^{\frac{1}{1-\omega}}\right)$ iterations, where $\omega\in(0,1)$ is the decay parameter of the learning rate, and $\gamma$ is the discount factor. Our analysis develops novel techniques to derive finite-time bounds on the difference between two inter-connected stochastic processes, which is new to the literature of stochastic approximation.

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