On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes
This addresses theoretical stability issues in GAN training for time-series data, but it is incremental as it focuses on a specific model class.
The paper investigates the existence of Nash equilibrium in moment-matching GANs for stationary Gaussian processes, showing that it depends on the discriminator family and generator symmetry, with conditions leading to non-existence, consistent non-Nash, or unique consistent Nash equilibrium.
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.