Distributed Primal–Dual Algorithms for Stochastic Generalized Nash Equilibrium Seeking Under Full and Partial-Decision Information
Lifeng Zheng, Huaqing Li, Liang Ran, Lan Gao, Dawen Xia · IEEE Transactions on Control of Network Systems · 2022
Motivated by practical applications involving randomness, e.g., the power market model, the transportation model, and the signal transmission model, this article investigates the stochastic generalized Nash equilibrium (SGNE) problem where the cost function of each player is influenced by a stochastic variable. Employing the operator splitting technique, stochastic approximation scheme, and variance reduction scheme, this article develops a distributed primal–dual algorithm with full-decision information for seeking the SGNE, in which a fully connected interference graph is used for transmitting information among players. Considering the case that players cannot know all other players' decisions, a distributed primal–dual algorithm with partial-decision information is proposed by introducing a local estimation to approximate the decision information of other players. It is proved that both algorithms converge to an SGNE provided that the uncoordinated fixed step sizes are less than the given upper bounds. Compared with existing algorithms, the algorithm with partial-decision information does not need the global game information. Each player is only required to know its local cost function, local feasible set, and a local block of the affine constraint, and share information with its neighbors. Numerical simulations are given for the networked Cournot competition and autonomous energy-management system to show the algorithm efficiency and performance.