  Generative Adversarial Networks (GANs) are one of the most practical methods
for learning data distributions. A popular GAN formulation is based on the use
of Wasserstein distance as a metric between probability distributions.
Unfortunately, minimizing the Wasserstein distance between the data
distribution and the generative model distribution is a computationally
challenging problem as its objective is non-convex, non-smooth, and even hard
to compute. In this work, we show that obtaining gradient information of the
smoothed Wasserstein GAN formulation, which is based on regularized Optimal
Transport (OT), is computationally effortless and hence one can apply first
order optimization methods to minimize this objective. Consequently, we
establish theoretical convergence guarantee to stationarity for a proposed
class of GAN optimization algorithms. Unlike the original non-smooth
formulation, our algorithm only requires solving the discriminator to
approximate optimality. We apply our method to learning MNIST digits as well as
CIFAR-10images. Our experiments show that our method is computationally
efficient and generates images comparable to the state of the art algorithms
given the same architecture and computational power.
