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arXiv · 1608.00039

Distributed Learning for Stochastic Generalized Nash Equilibrium Problems

Chung-Kai Yu·Mihaela van der Schaar·Ali H. Sayed
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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 $O(μ_\text{max})$, for small step-size value $μ_\text{max}$ and sufficiently large penalty parameters. The operation of the algorithm is illustrated by considering the network Cournot competition problem.

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Chung-Kai Yu, Mihaela van der Schaar, Ali H. Sayed. 2017-04-06. Distributed Learning for Stochastic Generalized Nash Equilibrium Problems. https://doi.org/10.1109/tsp.2017.2695451

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