Multi-Agent Optimization and Learning: A Non-Expansive Operators Perspective

TL;DR

This paper presents a unifying perspective on multi-agent optimization and learning algorithms using non-expansive operator theory, offering insights that could guide future research in the field.

Contribution

It introduces a novel framework that interprets various multi-agent algorithms through non-expansive operators, unifying diverse approaches under a common theoretical lens.

Findings

Provides a unifying theoretical framework for multi-agent algorithms

Highlights the role of non-expansive operators in convergence analysis

Suggests new directions for research based on the operator perspective

Abstract

Multi-agent systems are increasingly widespread in a range of application domains, with optimization and learning underpinning many of the tasks that arise in this context. Different approaches have been proposed to enable the cooperative solution of these optimization and learning problems, including first- and second-order methods, and dual (or Lagrangian) methods, all of which rely on consensus and message-passing. In this article we discuss these algorithms through the lens of non-expansive operator theory, providing a unifying perspective. We highlight the insights that this viewpoint delivers, and discuss how it can spark future original research.