Variance-Reduced Distributed Splitting Schemes for Stochastic Generalized Nash Equilibrium Seeking

In this work we focus on generalized Nash equilibrium seeking with expectation-valued operators. Accordingly, inspired by Tseng’s work for handling structured monotone inclusion problems, we propose a distributed modified forward-backward splitting algorithm based on variance reduction. The scheme features a Lipschitz continuous operator which is merely monotone. Notably, it allows for expectation-valued mappings and does not require strong monotonicity or cocoercivity assumptions on the mapping. We demonstrate that the proposed scheme ensures almost sure convergence. Our case study on a class of networked Cournot game further validate these findings and indicate good performance of the variance-reduced splitting schemes.