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

arXiv: https://arxiv.org/abs/2206.15177 · HTML: https://mlsanity.com/paper/2206.15177/

## 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.

## Builds on (most cited first, 24 of 24)

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- [Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile](https://mlsanity.com/paper/1807.02629/) (2018)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [GANSynth: Adversarial Neural Audio Synthesis](https://mlsanity.com/paper/1902.08710/) (2019)
- [Learning to Simulate Dynamic Environments with GameGAN](https://mlsanity.com/paper/2005.12126/) (2020)
- [The Complexity of Constrained Min-Max Optimization](https://mlsanity.com/paper/2009.09623/) (2020)
- [Finding Mixed Nash Equilibria of Generative Adversarial Networks](https://mlsanity.com/paper/1811.02002/) (2018)
- [Local Saddle Point Optimization: A Curvature Exploitation Approach](https://mlsanity.com/paper/1805.05751/) (2018)
- [A mean-field analysis of two-player zero-sum games](https://mlsanity.com/paper/2002.06277/) (2020)
- [Convergence Problems with Generative Adversarial Networks (GANs)](https://mlsanity.com/paper/1806.11382/) (2018)
- [Game on Random Environment, Mean-field Langevin System and Neural Networks](https://mlsanity.com/paper/2004.02457/) (2020)
- [Game Theoretic Optimization via Gradient-based Nikaido-Isoda Function](https://mlsanity.com/paper/1905.05927/) (2019)
- [On stochastic mirror descent with interacting particles: convergence properties and variance reduction](https://mlsanity.com/paper/2007.07704/) (2020)
- [On Characterizing GAN Convergence Through Proximal Duality Gap](https://mlsanity.com/paper/2105.04801/) (2021)
- [Local Nash Equilibria are Isolated, Strict Local Nash Equilibria in `Almost All' Zero-Sum Continuous Games](https://mlsanity.com/paper/2002.01007/) (2020)
- [Convergence of GANs Training: A Game and Stochastic Control Methodology](https://mlsanity.com/paper/2112.00222/) (2021)
- [Escaping from an attractor: Importance sampling and rest points I](https://mlsanity.com/paper/1303.0450/) (2013)
- [A large deviations analysis of certain qualitative properties of parallel tempering and infinite swapping algorithms](https://mlsanity.com/paper/1604.05703/) (2016)

## 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.