On Variance-Reduced Extragradient Methods for Stochastic Generalized Nash Equilibrium Problems

We study variance reduction schemes for stochastic generalized Nash equilibrium problems. Specifically, we consider two instances of the extragradient algorithm to find a Nash equilibrium and show their convergence under weaker assumptions than the literature. In the particular case where we can write the cost function as a finite sum, we also propose a novel approximation scheme that sensibly lowers the computational burden. Numerical simulations suggest that the performance of the new approximation scheme can improve the computations also in the fully stochastic (infinite) case.