Learning generalized Nash equilibria in monotone games: A hybrid adaptive extremum seeking control approach

TL;DR

This paper introduces a novel hybrid control approach for learning generalized Nash equilibria in monotone games, featuring a semi-decentralized algorithm, gain adaptation, and a data-driven variant, demonstrated on oil extraction optimization.

Contribution

It presents a new semi-decentralized algorithm for GNE learning, a gain adaptation scheme, and a data-driven method using zeroth-order information, advancing the state of the art in game equilibrium computation.

Findings

Successfully computes GNE in monotone games without projections.

Gain adaptation improves scaling and convergence.

Effective application to oil extraction optimization.

Abstract

In this paper, we solve the problem of learning a generalized Nash equilibrium (GNE) in merely monotone games. First, we propose a novel continuous semi-decentralized solution algorithm without projections that uses first-order information to compute a GNE with a central coordinator. As the second main contribution, we design a gain adaptation scheme for the previous algorithm in order to alleviate the problem of improper scaling of the cost functions versus the constraints. Third, we propose a data-driven variant of the former algorithm, where each agent estimates their individual pseudogradient via zeroth-order information, namely, measurements of their individual cost function values. Finally, we apply our method to a perturbation amplitude optimization problem in oil extraction engineering.