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

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.