Convergence Rate of Distributed Subgradient Methods under Communication Delays

Abstract

Motivated by broad applications in computer science and engineering, we study distributed algorithms for optimization problems over a network of nodes, where the goal is to optimize a global objective composed of a sum of local functions. In this paper, we consider a popular distributed gradient-based consensus algorithm, which only requires local computation and communication. A significant problem in this area is to analyze the convergence rate of such algorithms in the presence of communication delays that are inevitable in distributed systems. Our main contribution is to obtain an upper bound on the rate of convergence of the algorithm as a function of the network size, topology, and the inter-node communication delays.