Generative Adversarial Network: Some Analytical Perspectives

TL;DR

This paper provides an analytical overview of GANs, exploring their training via SDE approximations and applications in high-dimensional MFGs and mathematical finance, highlighting theoretical insights and practical implications.

Contribution

It offers a novel analytical perspective on GANs, including SDE-based training methods and applications in complex high-dimensional problems.

Findings

SDE approximations improve understanding of GAN training dynamics

GANs can be effectively applied to high-dimensional MFGs

Potential in mathematical finance applications

Abstract

Ever since its debut, generative adversarial networks (GANs) have attracted tremendous amount of attention. Over the past years, different variations of GANs models have been developed and tailored to different applications in practice. Meanwhile, some issues regarding the performance and training of GANs have been noticed and investigated from various theoretical perspectives. This subchapter will start from an introduction of GANs from an analytical perspective, then move on to the training of GANs via SDE approximations and finally discuss some applications of GANs in computing high dimensional MFGs as well as tackling mathematical finance problems.