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.
翻译:创世对抗网络在图像生成和处理方面取得了巨大成功,最近吸引了越来越多的金融模型兴趣。本文件从平均场游戏和最佳运输的角度分析了全球网络。更具体地说,从游戏理论角度,全球网络被解释为Pareto最佳标准或中场控制下的MFG;从最佳运输角度,全球网络将最大限度地降低发电机从已知的潜在潜在分布到未知数据真实分布的最好运输成本指数。GANs的MFGs观点导致以GAN为基础的计算方法(MFGANs)解决MFGs:后向的Hamilton-Jacobi-Bellman方程式的一个神经网络和前方Fokker-Planck方程式的一个神经网络,这两个神经网络都是以对抗方式培训的。数字实验显示,与现有的神经网络方法相比,这一拟议算法的性表现优异,特别是在较高维维度的案例中。