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Q-Learning in Regularized Mean-field Games

Author

Listed:
  • Berkay Anahtarci

    (Özyeğin University)

  • Can Deha Kariksiz

    (Özyeğin University)

  • Naci Saldi

    (Bilkent University)

Abstract

In this paper, we introduce a regularized mean-field game and study learning of this game under an infinite-horizon discounted reward function. Regularization is introduced by adding a strongly concave regularization function to the one-stage reward function in the classical mean-field game model. We establish a value iteration based learning algorithm to this regularized mean-field game using fitted Q-learning. The regularization term in general makes reinforcement learning algorithm more robust to the system components. Moreover, it enables us to establish error analysis of the learning algorithm without imposing restrictive convexity assumptions on the system components, which are needed in the absence of a regularization term.

Suggested Citation

  • Berkay Anahtarci & Can Deha Kariksiz & Naci Saldi, 2023. "Q-Learning in Regularized Mean-field Games," Dynamic Games and Applications, Springer, vol. 13(1), pages 89-117, March.
    • Handle: RePEc:spr:dyngam:v:13:y:2023:i:1:d:10.1007_s13235-022-00450-2
    DOI: 10.1007/s13235-022-00450-2
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    References listed on IDEAS

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    1. Piotr Więcek & Eitan Altman, 2015. "Stationary Anonymous Sequential Games with Undiscounted Rewards," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 686-710, August.
    2. Naci Saldi & Tamer Başar & Maxim Raginsky, 2019. "Approximate Nash Equilibria in Partially Observed Stochastic Games with Mean-Field Interactions," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1006-1033, August.
    3. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    4. A. Bensoussan & K. Sung & S. Yam, 2013. "Linear–Quadratic Time-Inconsistent Mean Field Games," Dynamic Games and Applications, Springer, vol. 3(4), pages 537-552, December.
    5. Adlakha, Sachin & Johari, Ramesh & Weintraub, Gabriel Y., 2015. "Equilibria of dynamic games with many players: Existence, approximation, and market structure," Journal of Economic Theory, Elsevier, vol. 156(C), pages 269-316.
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