Distributed quantized gradient-free algorithm for multi-agent convex optimization

Abstract

In this paper, we study a convex optimization problem that arises in a network where multiple agents cooperatively optimize the sum of nonsmooth but Lipschitz continuous functions, subject to a convex and compact constraint set. Under the additional constraint that each agent can only transmit quantized information, we develop a distributed quantized gradient-free algorithm for solving the multi-agent convex optimization problem over a time-varying network. In particular, we provide the convergence rate analysis results of the proposed algorithm, and highlight the dependence of the error bound on the smooth parameter and quantization resolution.