Zeroth-Order Feedback Optimization in Multi-Agent Systems: Tackling Coupled Constraints

TL;DR

This paper develops a distributed zeroth-order feedback optimization algorithm for multi-agent systems with coupled constraints, using gradient estimation and consensus techniques, and provides theoretical convergence analysis validated by experiments.

Contribution

It introduces a novel zeroth-order optimization method for multi-agent systems with coupled constraints, including convergence guarantees and complexity analysis.

Findings

The algorithm achieves sublinear convergence rate.

It effectively handles coupled constraints in distributed settings.

Numerical results confirm the theoretical predictions.

Abstract

This paper investigates distributed zeroth-order feedback optimization in multi-agent systems with coupled constraints, where each agent operates its local action vector and observes only zeroth-order information to minimize a global cost function subject to constraints in which the local actions are coupled. Specifically, we employ two-point zeroth-order gradient estimation with delayed information to construct stochastic gradients, and leverage the constraint extrapolation technique and the averaging consensus framework to effectively handle the coupled constraints. We also provide convergence rate and oracle complexity results for our algorithm, characterizing its computational efficiency and scalability by rigorous theoretical analysis. Numerical experiments are conducted to validate the algorithm's effectiveness.