Maxmin Q-learning: Controlling the Estimation Bias of Q-learning
This addresses a fundamental issue in reinforcement learning for researchers and practitioners, offering a method to mitigate bias that can improve learning efficiency, though it is incremental as it builds on existing Q-learning variants.
The paper tackles the overestimation bias in Q-learning by proposing Maxmin Q-learning, a generalization that allows flexible control of bias, and shows theoretically that it can achieve unbiased estimation with lower variance than Q-learning, while empirically achieving superior performance on benchmark problems.
Q-learning suffers from overestimation bias, because it approximates the maximum action value using the maximum estimated action value. Algorithms have been proposed to reduce overestimation bias, but we lack an understanding of how bias interacts with performance, and the extent to which existing algorithms mitigate bias. In this paper, we 1) highlight that the effect of overestimation bias on learning efficiency is environment-dependent; 2) propose a generalization of Q-learning, called \emph{Maxmin Q-learning}, which provides a parameter to flexibly control bias; 3) show theoretically that there exists a parameter choice for Maxmin Q-learning that leads to unbiased estimation with a lower approximation variance than Q-learning; and 4) prove the convergence of our algorithm in the tabular case, as well as convergence of several previous Q-learning variants, using a novel Generalized Q-learning framework. We empirically verify that our algorithm better controls estimation bias in toy environments, and that it achieves superior performance on several benchmark problems.