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A General Framework for Learning Mean-Field Games

Author

Listed:
  • Xin Guo

    (Industrial Engineering and Operations Research Department, University of California–Berkeley, Berkeley, California 94720; Amazon, Seattle, Washington 98109)

  • Anran Hu

    (Industrial Engineering and Operations Research Department, University of California–Berkeley, Berkeley, California 94720)

  • Renyuan Xu

    (Daniel J. Epstein Department of Industrial Systems & Engineering, Viterbi School of Engineering, University of Southern California, Los Angeles, California 90089; Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom)

  • Junzi Zhang

    (Amazon, Seattle, Washington 98109; Institute for Computational & Mathematical Engineering, Stanford University, California 94305)

Abstract
This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision making in stochastic games with a large population. It first establishes the existence of a unique Nash equilibrium to this GMFG, and it demonstrates that naively combining reinforcement learning with the fixed-point approach in classical mean-field games yields unstable algorithms. It then proposes value-based and policy-based reinforcement learning algorithms (GMF-V and GMF-P, respectively) with smoothed policies, with analysis of their convergence properties and computational complexities. Experiments on an equilibrium product pricing problem demonstrate that two specific instantiations of GMF-V with Q-learning and GMF-P with trust region policy optimization—GMF-V-Q and GMF-P-TRPO, respectively—are both efficient and robust in the GMFG setting. Moreover, their performance is superior in convergence speed, accuracy, and stability when compared with existing algorithms for multiagent reinforcement learning in the N -player setting.

Suggested Citation

  • Xin Guo & Anran Hu & Renyuan Xu & Junzi Zhang, 2023. "A General Framework for Learning Mean-Field Games," Mathematics of Operations Research, INFORMS, vol. 48(2), pages 656-686, May.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:2:p:656-686
    DOI: 10.1287/moor.2022.1274
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