Event-Triggered Distributed Stochastic Mirror Descent for Convex Optimization

• Published in: IEEE transaction on neural networks and learning systems Vol. 34; no. 9; pp. 6480 - 6491
• Main Authors: Xiong, Menghui, Zhang, Baoyong, Ho, Daniel W. C., Yuan, Deming, Xu, Shengyuan
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.09.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Bandwidth; Bregman divergence; Constraints; Convergence; Convex functions; Convexity; Distance measurement; distributed convex optimization; Divergence; event-triggered communication strategy; Machine learning algorithms; Mirrors; Multiagent systems; Optimization; stochastic mirror descent algorithm; Stochasticity; Upper bound; Upper bounds
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2021.3137010

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.