Learning generalized Nash equilibria in multi-agent dynamical systems via extremum seeking control

TL;DR

This paper introduces a continuous-time algorithm for learning generalized Nash equilibria in multi-agent systems, including a data-driven extremum seeking variant, applicable to systems with nonlinear dynamics and real-world applications.

Contribution

It presents a novel continuous-time algorithm for GNE learning, including a zero-order data-driven extremum seeking approach for multi-agent systems with nonlinear dynamics.

Findings

Effective convergence in strongly monotone games

Successful application to robotic sensor networks

Distributed wind farm optimization results

Abstract

In this paper, we consider the problem of learning a generalized Nash equilibrium (GNE) in strongly monotone games. First, we propose a novel continuous-time solution algorithm that uses regular projections and first-order information. As second main contribution, we design a data-driven variant of the former algorithm where each agent estimates their individual pseudo-gradient via zero-order information, namely, measurements of their individual cost function values, as typical of extremum seeking control. Third, we generalize our setup and results for multi-agent systems with nonlinear dynamics. Finally, we apply our algorithms to connectivity control in robotic sensor networks and distributed wind farm optimization.