Zeroth Order Nonconvex Multi-Agent Optimization over Networks

TL;DR

This paper introduces distributed algorithms for non-convex multi-agent optimization where agents only have access to function values, not gradients, and analyzes their convergence over various network topologies.

Contribution

It presents the first zeroth-order distributed algorithms for non-convex problems with convergence guarantees over different network structures.

Findings

Algorithms converge to stationary solutions

Efficient performance demonstrated through numerical experiments

Applicable to undirected and star network topologies

Abstract

In this paper, we consider distributed optimization problems over a multi-agent network, where each agent can only partially evaluate the objective function, and it is allowed to exchange messages with its immediate neighbors. Differently from all existing works on distributed optimization, our focus is given to optimizing a class of non-convex problems, and under the challenging setting where each agent can only access the zeroth-order information (i.e., the functional values) of its local functions. For different types of network topologies such as undirected connected networks or star networks, we develop efficient distributed algorithms and rigorously analyze their convergence and rate of convergence (to the set of stationary solutions). Numerical results are provided to demonstrate the efficiency of the proposed algorithms.