Revisiting EXTRA for Smooth Distributed Optimization

Abstract

EXTRA is a popular method for dencentralized distributed optimization and has broad applications. This paper revisits EXTRA. First, we give a sharp complexity analysis for EXTRA with the improved O((L+11-_2(W))1(1-_2(W))) communication and computation complexities for -strongly convex and L-smooth problems, where _2(W) is the second largest singular value of the weight matrix W. When the strong convexity is absent, we prove the O((L+11-_2(W))11-_2(W)) complexities. Then, we use the Catalyst framework to accelerate EXTRA and obtain the O(L(1-_2(W)) L(1-_2(W))1) communication and computation complexities for strongly convex and smooth problems and the O(L(1-_2(W))1(1-_2(W))) complexities for non-strongly convex ones. Our communication complexities of the accelerated EXTRA are only worse by the factors of (L(1-_2(W))) and (1(1-_2(W))) from the lower complexity bounds for strongly convex and non-strongly convex problems, respectively.

Tasks

Reproductions