Game on Random Environment, Mean-Field Langevin System, and Neural Networks
研究了一类由相对熵正则化的博弈，其中玩家策略通过随机环境耦合，证明了均衡的存在唯一性及平均场朗之万系统收敛性，并应用于深度神经网络的随机梯度下降和生成对抗网络分析。
In this paper, we study a class of games regularized by relative entropy where the players’ strategies are coupled through a random environment. Besides existence and uniqueness of equilibria for such games, we prove, under different sets of hypotheses that the marginal laws of the corresponding mean-field Langevin systems can converge toward the games’ equilibria. As an application, we show that dynamic games fall in this framework by considering the time horizon as environment. Concerning applications, our results allow analysis of stochastic gradient descent algorithms for deep neural networks in the context of supervised learning and for generative adversarial networks.