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Large deviations for interacting particle dynamics for finding mixed equilibria in zero-sum games

arXiv 2206.15177 ↗First posted 30 Jun 2022stat.ML cs.LG math.OCcited by 0

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Abstract (arXiv)

Finding equilibrium points in continuous minmax games has become a key problem within machine learning, in part due to its connection to the training of generative adversarial networks and reinforcement learning. Because of existence and robustness issues, recent developments have shifted from pure equilibria to focusing on mixed equilibrium points. In this work we consider a method for finding mixed equilibria in two-layer zero-sum games based on entropic regularisation, where the two competing strategies are represented by two sets of interacting particles. We show that the sequence of empirical measures of the particle system satisfies a large deviation principle as the number of particles grows to infinity, and how this implies convergence of the empirical measure and the associated Nikaido-Isoda error, complementing existing law of large numbers results.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 24 of its 56 references that are in the map. First posted on arXiv 30 Jun 2022.

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References · 24

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12 more
  1. 2018Finding Mixed Nash Equilibria of Generative Adversarial Networkscited by 49
  2. 2018Local Saddle Point Optimization: A Curvature Exploitation Approachcited by 28
  3. 2020A mean-field analysis of two-player zero-sum gamescited by 28
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  9. 2020Local Nash Equilibria are Isolated, Strict Local Nash Equilibria in `Almost All' Zero-Sum Continuous Gamescited by 2
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