论文标题
关于在零和游戏中找到混合平衡的相互作用粒子动力学的大偏差的注释
A note on large deviations for interacting particle dynamics for finding mixed equilibria in zero-sum games
论文作者
论文摘要
在连续的minimax游戏中找到平衡点已成为机器学习中的关键问题，部分原因是它与生成对抗网络的培训有关。由于存在和鲁棒性问题，最近的发展已经从纯平的平衡转变为专注于混合平衡点。在本说明中，我们考虑了Domingo-Enrich等人提出的一种方法。在两层零和游戏中找到混合平衡。该方法基于熵正则化，两种竞争策略由两组相互作用的粒子表示。我们表明，随着颗粒的数量增长到无穷大，粒子系统的经验度量序列满足了一个较大的偏差原理，以及这意味着经验度量的收敛性和相关的Nikaidô-Isoda误差，补充了大量结果的现有定律。
Finding equilibria points in continuous minimax games has become a key problem within machine learning, in part due to its connection to the training of generative adversarial networks. Because of existence and robustness issues, recent developments have shifted from pure equilibria to focusing on mixed equilibria points. In this note we consider a method proposed by Domingo-Enrich et al. for finding mixed equilibria in two-layer zero-sum games. The method is based on entropic regularisation and 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 Nikaidô-Isoda error, complementing existing law of large numbers results.
