Event-Triggered Distributed Stochastic Mirror Descent for Convex Optimization

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.

Automated summary

This article investigates distributed convex constrained optimization over a time-varying multiagent network in the non-Euclidean sense, taking into account the bandwidth limitation of the network. An event-triggered strategy is applied to reduce communication costs, and a distributed stochastic mirror descent algorithm based on event triggers is developed to solve the multiagent optimization problem subject to a convex constraint. The convergence of the algorithm is also analyzed, with an upper bound established for each agent's convergence result, which depends on the trigger threshold.