An Accelerated Gossip-Based Distributed Gradient Method

This paper studies distributed optimization over the multi-agent network. We develop and analyze a novel accelerated distributed gradient descent method, termed as G-DGDlm, for gossip communication protocol. G-DGDlm uses gradient tracking technique and local memory. Specifically, each agent stores two past variables, namely, an estimate of the average gradient and an estimate of the optimal solution. G-DGDlm achieves linear convergence for strongly convex and smooth functions when the positive fixed stepsize is sufficiently small and the coefficient θ of past variables is $0 < \theta \leq 3 - 2\sqrt 2 $. Compared to the related works, we remove the dependence of θ on global parameters and G-DGDlm is applicable to gossip communication protocol. Numerical experiments of distributed estimation in sensor networks show the faster convergence speed of G-DGDlm in comparison with the state-of-the-art methods.