Distributed Learning for Stochastic Generalized Nash Equilibrium Problems

• Published in: IEEE transactions on signal processing Vol. 65; no. 15; pp. 3893 - 3908
• Main Authors: Chung-Kai Yu, van der Schaar, Mihaela, Sayed, Ali H.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-08-2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive learning; Algorithms; Competition; Cost function; Coupling; diffusion learning; Distance learning; Economic analysis; Economic models; Equilibrium; Game theory; generalized Nash equilibrium; Learning; Marketing; Nash equilibrium; Network topology; penalized approximation; Probability theory; Randomness; Resource management; Signal processing algorithms; Stochastic processes
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2017.2695451

This paper examines a stochastic formulation of the generalized Nash equilibrium problem where agents are subject to randomness in the environment of unknown statistical distribution. We focus on fully distributed online learning by agents and employ penalized individual cost functions to deal with coupled constraints. Three stochastic gradient strategies are developed with constant step-sizes. We allow the agents to use heterogeneous step-sizes and show that the penalty solution is able to approach the Nash equilibrium in a stable manner within O(μ max ), for small step-size value μ max and sufficiently large penalty parameters. The operation of the algorithm is illustrated by considering the network Cournot competition problem.