RegQ: Convergent Q-Learning with Linear Function Approximation using Regularization

Han-Dong Lim, Do Wan Kim, Donghwan Lee

Keywords: reinforcement learning, Q-learning, reinforcement learning theory

TL;DR: This paper develops convergent Q-learning algorithm when linear function approximation is used.

Abstract: Q-learning is widely used algorithm in reinforcement learning community. Under the lookup table setting, its convergence is well established. However, its behavior is known to be unstable with the linear function approximation case. This paper develops a new Q-learning algorithm, called RegQ, that converges when linear function approximation is used. We prove that simply adding an appropriate regularization term ensures convergence of the algorithm. We prove its stability using a recent analysis tool based on switching system models. Moreover, we experimentally show that RegQ converges in environments where Q-learning with linear function approximation has known to diverge. We also provide an error bound on the solution where the algorithm converges.

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