Optimal Decentralized Composite Optimization for Convex Functions

Abstract

In this paper, we focus on the decentralized composite optimization for convex functions. Because of advantages such as robust to the network and no communication bottle-neck in the central server, the decentralized optimization has attracted much research attention in signal processing, control, and optimization communities. Many optimal algorithms have been proposed for the objective function is smooth and (strongly)-convex in the past years. However, it is still an open question whether one can design an optimal algorithm when there is a non-smooth regularization term. In this paper, we fill the gap between smooth decentralized optimization and decentralized composite optimization and propose the first algorithm which can achieve both the optimal computation and communication complexities. Our experiments also validate the effectiveness and efficiency of our algorithm both in computation and communication.