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Continuous Time Learning Algorithms in Optimization and Game Theory

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  • Sylvain Sorin

    (Sorbonne Université, Campus P.&M. Curie)

Abstract

The purpose of this work is the comparison of learning algorithms in continuous time used in optimization and game theory. The first three are issued from no-regret dynamics and cover in particular “Replicator dynamics” and “Local projection dynamics”. Then we study “Conditional gradient” versus “Global projection” dynamics and finally “Frank-Wolfe” versus “Best reply” dynamics. Important similarities occur when considering potential or dissipative games.

Suggested Citation

  • Sylvain Sorin, 2023. "Continuous Time Learning Algorithms in Optimization and Game Theory," Dynamic Games and Applications, Springer, vol. 13(1), pages 3-24, March.
    • Handle: RePEc:spr:dyngam:v:13:y:2023:i:1:d:10.1007_s13235-021-00423-x
    DOI: 10.1007/s13235-021-00423-x
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    References listed on IDEAS

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    1. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2006. "Stochastic Approximations and Differential Inclusions, Part II: Applications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 673-695, November.
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    7. H. Attouch & M. Teboulle, 2004. "Regularized Lotka-Volterra Dynamical System as Continuous Proximal-Like Method in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 541-570, June.
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    9. Rustichini, Aldo, 1999. "Optimal Properties of Stimulus--Response Learning Models," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 244-273, October.
    10. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
    11. Panayotis Mertikopoulos & William H. Sandholm, 2016. "Learning in Games via Reinforcement and Regularization," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1297-1324, November.
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    13. Josef Hofbauer & Sylvain Sorin & Yannick Viossat, 2009. "Time Average Replicator and Best-Reply Dynamics," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 263-269, May.
    14. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.4, July.
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    20. Sandholm, William H. & DokumacI, Emin & Lahkar, Ratul, 2008. "The projection dynamic and the replicator dynamic," Games and Economic Behavior, Elsevier, vol. 64(2), pages 666-683, November.
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    24. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2012. "Perturbations of Set-Valued Dynamical Systems, with Applications to Game Theory," Dynamic Games and Applications, Springer, vol. 2(2), pages 195-205, June.
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    26. Sylvain Sorin & Cheng Wan, 2016. "Finite composite games: Equilibria and dynamics," Post-Print hal-02885860, HAL.
    27. Lahkar, Ratul & Sandholm, William H., 2008. "The projection dynamic and the geometry of population games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 565-590, November.
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