  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.
