Extremum Seeking Tracking for Derivative-free Distributed Optimization

TL;DR

This paper introduces a novel distributed optimization algorithm that enables agents to cooperatively minimize unknown local functions using only local measurements, combining extremum seeking and gradient tracking techniques for accurate solutions.

Contribution

It proposes a new distributed method integrating extremum seeking with gradient tracking to optimize unknown functions without gradient information.

Findings

Converges to arbitrarily accurate solutions

Effective in personalized optimization scenarios

Validated through numerical simulations

Abstract

In this paper, we deal with a network of agents that want to cooperatively minimize the sum of local cost functions depending on a common decision variable. We consider the challenging scenario in which objective functions are unknown and agents have only access to local measurements of their local functions. We propose a novel distributed algorithm that combines a recent gradient tracking policy with an extremum seeking technique to estimate the global descent direction. The joint use of these two techniques results in a distributed optimization scheme that provides arbitrarily accurate solution estimates through the combination of Lyapunov and averaging analysis approaches with consensus theory. We perform numerical simulations in a personalized optimization framework to corroborate the theoretical results.