Zeroth-Order Feedback Optimization for Cooperative Multi-Agent Systems

TL;DR

This paper introduces a zeroth-order feedback optimization method for cooperative multi-agent systems where gradient information is unavailable, providing complexity bounds and demonstrating effectiveness through a routing control example.

Contribution

The paper proposes a novel zeroth-order optimization scheme for multi-agent systems and analyzes its complexity in convex and nonconvex scenarios with noisy and noiseless data.

Findings

Explicit complexity bounds for the proposed method.

Effective performance demonstrated in distributed routing control.

Applicable to both convex and nonconvex problems.

Abstract

We study a class of cooperative multi-agent optimization problems, where each agent is associated with a local action vector and a local cost, and the goal is to cooperatively find the joint action profile that minimizes the average of the local costs. Such problems arise in many applications, such as distributed routing control, wind farm operation, etc. In many of these problems, gradient information may not be readily available, and the agents may only observe their local costs incurred by their actions as a feedback to determine their new actions. In this paper, we propose a zeroth-order feedback optimization scheme for the class of problems we consider, and provide explicit complexity bounds for both the convex and nonconvex settings with noiseless and noisy local cost observations. We also discuss briefly on the impacts of knowledge of local function dependence between agents. The algorithm's performance is justified by a numerical example of distributed routing control.