2020/10/17 by Barbara Franci, Franci, Barbara, Sergio Grammatico +1
Computer Science · Mathematics · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #cs.GT #cs.LG #math.OC
paper · pdf · doi:10.48550/arxiv.2010.10013
arXiv admin note: text overlap with arXiv:2003.13637
arxiv created 2021/05/21 · arxiv updated 2021/05/24
Generative adversarial networks (GANs) are a class of generative models with two antagonistic neural networks: a generator and a discriminator. These two neural networks compete against each other through an adversarial process that can be modeled as a stochastic Nash equilibrium problem. Since the associated training process is challenging, it is fundamental to design reliable algorithms to compute an equilibrium. In this paper, we propose a stochastic relaxed forward-backward (SRFB) algorithm for GANs and we show convergence to an exact solution when an increasing number of data is available. We also show convergence of an averaged variant of the SRFB algorithm to a neighborhood of the solution when only few samples are available. In both cases, convergence is guaranteed when the pseudogradient mapping of the game is monotone. This assumption is among the weakest known in the literature. Moreover, we apply our algorithm to the image generation problem.