连接生成对抗网络、平均场博弈与最优传输
Connecting GANs, MFGs, and OT
AI总结：
本文从平均场博弈和最优传输视角分析GANs，提出基于GAN的MFGANs方法，用两个对抗训练的神经网络分别求解HJB方程和Fokker-Planck方程，在高维场景下性能优于现有方法。
摘要：
生成对抗网络（GANs）在图像生成与处理领域取得了巨大成功，近年来在金融建模中也引起了越来越多的关注。本文从平均场博弈（MFGs）和最优传输（OT）的视角分析GANs。具体而言，从博弈论视角看，GANs被解释为帕累托最优性准则下的平均场博弈或平均场控制；从最优传输视角看，GANs旨在将由生成器参数化的最优传输成本最小化，该成本度量从已知隐分布到未知真实数据分布之间的传输。GANs的平均场博弈视角引出了一个基于GAN的计算方法（MFGANs）来求解平均场博弈：一个神经网络用于反向Hamilton-Jacobi-Bellman方程，另一个神经网络用于正向Fokker-Planck方程，两个神经网络以对抗方式进行训练。数值实验表明，与现有神经网络方法相比，该算法表现出优越的性能，尤其是在高维情况下。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
