2018/02/21 by Maziar Sanjabi, Sanjabi, Maziar, Jimmy Ba +5 · 11 citations
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Generative Adversarial Networks and Image Synthesis #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Optimization and Control (math.OC) #cs.LG #math.OC #stat.ML
paper · pdf · doi:10.48550/arxiv.1802.08249
openalex publication_date 2018/02/21 · arxiv created 2018/05/22 · arxiv updated 2018/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.