Generative adversarial networks (GANs) are a widely used framework for learning generative models. Wasserstein GANs (WGANs), one of the most successful variants of GANs, require solving a minmax problem to global optimality, but in practice, are successfully trained with stochastic gradient descent-ascent. In this paper, we show that, when the generator is a one-layer network, stochastic gradient descent-ascent converges to a global solution in polynomial time and sample complexity.
We show that stochastic gradient descent ascent converges to a global optimum for WGAN with one-layer generator network. Attempts to prove that the Stochastic Gradient Decent-Ascent could converge to a global solution for the min-max problem of WGAN.