论文标题
连接gan，mfgs和ot
Connecting GANs, MFGs, and OT
论文作者
论文摘要
生成的对抗网络（GAN）在图像生成和处理方面取得了巨大的成功，并且最近引起了人们对金融模型的不断增长的兴趣。本文从平均场地游戏（MFG）和最佳运输的角度分析了甘恩。更具体地说，从游戏理论的角度来看，甘恩被解释为在帕累托最佳标准或均值场控制下的MFG。从最佳的传输角度来看，甘恩斯将发电机从已知的潜在分布到数据的未知分布索引的最佳运输成本最小化。 MFG的GAN观点导致基于GAN的计算方法（MFGANS）来解决MFGS：向后汉密尔顿 - 雅各比 - 贝尔曼方程的一个神经网络和一个用于前向fokker-Planck方程的神经网络，并在两个神经网络中受过两个神经网络的培训。数值实验表明，与现有的神经网络方法相比，该提出的算法的卓越性能，尤其是在较高维度的情况下。
Generative adversarial networks (GANs) have enjoyed tremendous success in image generation and processing, and have recently attracted growing interests in financial modelings. This paper analyzes GANs from the perspectives of mean-field games (MFGs) and optimal transport. More specifically, from the game theoretical perspective, GANs are interpreted as MFGs under Pareto Optimality criterion or mean-field controls; from the optimal transport perspective, GANs are to minimize the optimal transport cost indexed by the generator from the known latent distribution to the unknown true distribution of data. The MFGs perspective of GANs leads to a GAN-based computational method (MFGANs) to solve MFGs: one neural network for the backward Hamilton-Jacobi-Bellman equation and one neural network for the forward Fokker-Planck equation, with the two neural networks trained in an adversarial way. Numerical experiments demonstrate superior performance of this proposed algorithm, especially in the higher dimensional case, when compared with existing neural network approaches.
