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Entropy Regularization for Mean Field Games with Learning

Author

Listed:
  • Xin Guo

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720; Tsinghua-UC Berkeley Shenzhen Institute, Shenzhen 518055, China)

  • Renyuan Xu

    (Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90089; Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom)

  • Thaleia Zariphopoulou

    (Departments of Mathematics and IROM, The University of Texas at Austin, Austin, Texas 78712)

Abstract

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.

Suggested Citation

  • Xin Guo & Renyuan Xu & Thaleia Zariphopoulou, 2022. "Entropy Regularization for Mean Field Games with Learning," Mathematics of Operations Research, INFORMS, vol. 47(4), pages 3239-3260, November.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:4:p:3239-3260
    DOI: 10.1287/moor.2021.1238
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