Mean Field Game GAN

TL;DR

This paper introduces a new GAN framework based on mean field games, utilizing the Hopf formula to enable flexible, constraint-free training via neural networks, validated through experiments.

Contribution

It presents a novel MFG-based GAN model that employs the Hopf formula for flexible, constraint-free training, advancing the theoretical and practical aspects of generative modeling.

Findings

Model effectively trains via neural networks and samples.

Mathematically avoids Lipschitz-1 constraint.

Validated through multiple experiments.

Abstract

We propose a novel mean field games (MFGs) based GAN(generative adversarial network) framework. To be specific, we utilize the Hopf formula in density space to rewrite MFGs as a primal-dual problem so that we are able to train the model via neural networks and samples. Our model is flexible due to the freedom of choosing various functionals within the Hopf formula. Moreover, our formulation mathematically avoids Lipschitz-1 constraint. The correctness and efficiency of our method are validated through several experiments.