Zeroth-order Feedback Optimization for Cooperative Multi-Agent Systems

Abstract

We consider a class of multi-agent optimization problems, where each agent is associated with an action vector and a local cost that depends on the joint actions of all agents, and the goal is to minimize the average of the local costs. Such problems arise in many control applications such as wind farm operation and mobile sensor coverage. In many of these applications, while we have access to (zeroth-order) information about function values, it can be difficult to obtain (first-order) gradient information. In this paper, we propose a zeroth-order feedback optimization (ZFO) algorithm based on two-point gradient estimators for the considered class of problems, and provide the convergence rate to a first-order stationary point for nonconvex problems. We complement our theoretical analysis with numerical simulations on a wind farm power maximization problem.