Distributed Stochastic Consensus Optimization Using Communication-Censoring Strategy

In this article, a novel communication-efficient distributed stochastic algorithm (CO-DSA) is proposed for solving large-scale consensus optimization problems. As compared to the existing relevant work where only a sublinear convergence rate is obtained for strongly convex and smooth objective functions, the CO-DSA achieves a linear convergence rate even in the presence of an event-triggered communication-censoring strategy. Moreover, by properly setting the threshold function of the event-triggered communication scheme, the CO-DSA maintains the same convergence rate as the algorithm without event-triggered communication. This means the CO-DSA theoretically yields communication efficiency for free. Numerical experiments verify the theoretical findings and also show the excellent communication saving effect of the CO-DSA in large distributed networks.