Distributed Learning for Stochastic Generalized Nash Equilibrium Problems

Abstract

This work examines a stochastic formulation of the generalized Nash equilibrium problem (GNEP) 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 $O({\mu }_{\text{max}})$, for small step-size value ${\mu }_{\text{max}}$ and sufficiently large penalty parameters. The operation of the algorithm is illustrated by considering the network Cournot competition problem.

References in corpus (2)

• Distributed Consensus Algorithms in Sensor Networks: Link Failures and Channel Noise
• Learning in games with continuous action sets and unknown payoff functions

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