Model-Free Aggregative Cooperative Optimization via Randomized Gradient-Free Minimization and Exploration Momentum

TL;DR

This paper introduces ARGFree, a novel gradient-free algorithm for distributed aggregative optimization, with an improved variant ARGFree-EM that uses momentum to enhance high-dimensional performance.

Contribution

The paper presents the first gradient-free method for aggregative cooperative optimization, combining finite differences with tracking variables and momentum for better accuracy.

Findings

ARGFree converges in expectation to an approximate optimizer.

ARGFree-EM improves accuracy in high-dimensional settings.

The methods are applicable without gradient information in distributed systems.

Abstract

Aggregative cooperative optimization problems arise in distributed decision-making settings where each agent's objective depends on its own decision as well as on an aggregate variable capturing global system behavior. Motivated by practical scenarios where gradient information is unavailable, this paper introduces a randomized gradient-free algorithm, named ARGFree, for solving such problems. ARGFree combines finite-difference gradient approximations with a set of tracking variables, emulating the behavior of a gradient-based method. We prove that ARGFree converges in expectation to an approximate optimizer, with the approximation error stemming from the use of a randomized gradient estimator. To enhance performance in high-dimensional settings, we further propose an improved variant, ARGFree-EM, which incorporates momentum in the exploration signals to smooth sudden fluctuations in the gradient exploration signals and thereby improve the accuracy of the underlying distributed tracking mechanism. To the best of our knowledge, the class of ARGFree methods is the first in the literature capable of solving aggregating cooperative optimization problems without gradient information.