Event-Triggered Distributed Stochastic Mirror Descent for Convex Optimization
Menghui Xiong, Baoyong Zhang, Daniel W. C. Ho, Deming Yuan, Shengyuan Xu
Abstract
This article is concerned with the distributed convex constrained optimization over a time-varying multiagent network in the non-Euclidean sense, where the bandwidth limitation of the network is considered. To save the network resources so as to reduce the communication costs, we apply an event-triggered strategy (ETS) in the information interaction of all the agents over the network. Then, an event-triggered distributed stochastic mirror descent (ET-DSMD) algorithm, which utilizes the Bregman divergence as the distance-measuring function, is presented to investigate the multiagent optimization problem subject to a convex constraint set. Moreover, we also analyze the convergence of the developed ET-DSMD algorithm. An upper bound for the convergence result of each agent is established, which is dependent on the trigger threshold. It shows that a sublinear upper bound can be guaranteed if the trigger threshold converges to zero as time goes to infinity. Finally, a distributed logistic regression example is provided to prove the feasibility of the developed ET-DSMD algorithm.