Entropy Regularization for Mean Field Games with Learning

Entropy regularization has been extensively adopted to improve the efficiency, the stability, and the convergence of algorithms in reinforcement learning. This paper analyzes both quantitatively and qualitatively the impact of entropy regularization for mean field games (MFGs) with learning in a finite time horizon. Our study provides a theoretical justification that entropy regularization yields time-dependent policies and, furthermore, helps stabilizing and accelerating convergence to the game equilibrium. In addition, this study leads to a policy-gradient algorithm with exploration in MFG. With this algorithm, agents are able to learn the optimal exploration scheduling, with stable and fast convergence to the game equilibrium.