Stochastic Generalized Nash Equilibrium Seeking: Reflected Gradient Methods

This article concerns the stochastic generalized Nash equilibrium problem (NEP) characterized by uncertain expected value cost functions and shared constraints. In a full-decision information setting, we develop a novel distributed stochastic reflected forward–backward (FB) algorithm, which requires that each agent has access to the others’ decisions. Considering that agents only know the decisions from their immediate neighbors, a distributed stochastic RFB (SRFB) algorithm under partial-decision information is proposed. By recasting the problem as a monotone inclusion problem, both algorithms almost surely converge to a stochastic generalized Nash equilibrium by combining the stochastic approximation scheme and the variance reduction scheme. Finally, the numerical experiment validates the feasibility of the proposed algorithms and confirms the correctness of the theory.