Asynchronous Gossip-Based Gradient-Free Method for Multiagent Optimization

Abstract

This paper considers the constrained multiagent optimization problem. The objective function of the problem is a sum of convex functions, each of which is known by a specific agent only. For solving this problem, we propose an asynchronous distributed method that is based on gradient-free oracles and gossip algorithm. In contrast to the existing work, we do not require that agents be capable of computing the subgradients of their objective functions and coordinating their step size values as well. We prove that with probability 1 the iterates of all agents converge to the same optimal point of the problem, for a diminishing step size.