Diffusion Optimistic Learning for Min-Max Optimization

This work introduces and studies the convergence of a stochastic diffusion-optimistic learning (DOL) strategy for solving distributed nonconvex (NC) and Polyak-Lojasiewicz (PL) min-max optimization problems. Problems of this type are of interest due to a wide range of applications, including in generative adversarial networks (GANs), adversarial machine learning, and reinforcement learning. We prove that the DOL algorithm approaches an ε-stationary point through cooperation among agents following a left-stochastic communication protocol. The good performance of the proposed algorithm is illustrated by means of computer simulations.