On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes

Sixin Zhang
Proceedings of Mathematical and Scientific Machine Learning, PMLR 190:113-128, 2022.

Abstract

Generative Adversarial Networks (GANs) learn an implicit generative model from data samples through a two-player game. In this paper, we study the existence of Nash equilibrium of the game which is consistent as the number of data samples grows to infinity. In a realizable setting where the goal is to estimate the ground-truth generator of a stationary Gaussian process, we show that the existence of consistent Nash equilibrium depends crucially on the choice of the discriminator family. The discriminator defined from second-order statistical moments can result in non-existence of Nash equilibrium, existence of consistent non-Nash equilibrium, or existence and uniqueness of consistent Nash equilibrium, depending on whether symmetry properties of the generator family are respected. We further study empirically the local stability and global convergence of gradient descent-ascent methods towards consistent equilibrium.

Cite this Paper

BibTeX
@InProceedings{pmlr-v190-zhang22a, title = {On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes}, author = {Zhang, Sixin}, booktitle = {Proceedings of Mathematical and Scientific Machine Learning}, pages = {113--128}, year = {2022}, editor = {Dong, Bin and Li, Qianxiao and Wang, Lei and Xu, Zhi-Qin John}, volume = {190}, series = {Proceedings of Machine Learning Research}, month = {15--17 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v190/zhang22a/zhang22a.pdf}, url = {https://proceedings.mlr.press/v190/zhang22a.html}, abstract = {Generative Adversarial Networks (GANs) learn an implicit generative model from data samples through a two-player game. In this paper, we study the existence of Nash equilibrium of the game which is consistent as the number of data samples grows to infinity. In a realizable setting where the goal is to estimate the ground-truth generator of a stationary Gaussian process, we show that the existence of consistent Nash equilibrium depends crucially on the choice of the discriminator family. The discriminator defined from second-order statistical moments can result in non-existence of Nash equilibrium, existence of consistent non-Nash equilibrium, or existence and uniqueness of consistent Nash equilibrium, depending on whether symmetry properties of the generator family are respected. We further study empirically the local stability and global convergence of gradient descent-ascent methods towards consistent equilibrium.} }
Endnote
%0 Conference Paper %T On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes %A Sixin Zhang %B Proceedings of Mathematical and Scientific Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Bin Dong %E Qianxiao Li %E Lei Wang %E Zhi-Qin John Xu %F pmlr-v190-zhang22a %I PMLR %P 113--128 %U https://proceedings.mlr.press/v190/zhang22a.html %V 190 %X Generative Adversarial Networks (GANs) learn an implicit generative model from data samples through a two-player game. In this paper, we study the existence of Nash equilibrium of the game which is consistent as the number of data samples grows to infinity. In a realizable setting where the goal is to estimate the ground-truth generator of a stationary Gaussian process, we show that the existence of consistent Nash equilibrium depends crucially on the choice of the discriminator family. The discriminator defined from second-order statistical moments can result in non-existence of Nash equilibrium, existence of consistent non-Nash equilibrium, or existence and uniqueness of consistent Nash equilibrium, depending on whether symmetry properties of the generator family are respected. We further study empirically the local stability and global convergence of gradient descent-ascent methods towards consistent equilibrium.
APA
Zhang, S.. (2022). On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes. Proceedings of Mathematical and Scientific Machine Learning, in Proceedings of Machine Learning Research 190:113-128 Available from https://proceedings.mlr.press/v190/zhang22a.html.

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