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Near-optimal no-regret algorithms for zero-sum games

Author

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  • Daskalakis, Constantinos
  • Deckelbaum, Alan
  • Kim, Anthony

Abstract

We propose a new no-regret learning algorithm. When used against an adversary, our algorithm achieves average regret that scales optimally as O(1T) with the number T of rounds. However, when our algorithm is used by both players of a zero-sum game, their average regret scales as O(ln⁡TT), guaranteeing a near-linear rate of convergence to the value of the game. This represents an almost-quadratic improvement on the rate of convergence to the value of a zero-sum game known to be achievable by any no-regret learning algorithm. Moreover, it is essentially optimal as we also show a lower bound of Ω(1T) for all distributed dynamics, as long as the players do not know their payoff matrices in the beginning of the dynamics. (If they did, they could privately compute minimax strategies and play them ad infinitum.)

Suggested Citation

  • Daskalakis, Constantinos & Deckelbaum, Alan & Kim, Anthony, 2015. "Near-optimal no-regret algorithms for zero-sum games," Games and Economic Behavior, Elsevier, vol. 92(C), pages 327-348.
    • Handle: RePEc:eee:gamebe:v:92:y:2015:i:c:p:327-348
    DOI: 10.1016/j.geb.2014.01.003
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    References listed on IDEAS

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    Cited by:

    1. Simina Br^anzei & Nikhil R. Devanur & Yuval Rabani, 2019. "Proportional Dynamics in Exchange Economies," Papers 1907.05037, arXiv.org, revised Sep 2023.

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    More about this item

    Keywords

    Zero-sum games; Repeated games; Learning; No-regret dynamics;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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