论文标题
在随机环境，平均场兰格文系统和神经网络上进行游戏
Game on Random Environment, Mean-field Langevin System and Neural Networks
论文作者
论文摘要
在本文中，我们研究了一种由相对熵正规化的游戏，其中玩家的策略通过随机环境变量耦合。除了这种游戏平衡的存在和唯一性外，我们还证明，相应的平均范围Langevin Systems的边际定律可以在不同的环境中汇聚到游戏的平衡。作为应用程序，当人们将时间范围视为环境时，可以将动态游戏视为随机环境的游戏。实际上，我们的结果可以应用于在监督学习以及生成的对抗网络的背景下，分析深神经网络的随机梯度下降算法。
In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence and the uniqueness of equilibria of such games, we prove that the marginal laws of the corresponding mean-field Langevin systems can converge towards the games' equilibria in different settings. As applications, the dynamic games can be treated as games on a random environment when one treats the time horizon as the environment. In practice, our results can be applied to analysing the stochastic gradient descent algorithm for deep neural networks in the context of supervised learning as well as for the generative adversarial networks.
