Distributed Online Push-Sum Dual Averaging for Composite Optimization With Communication Delays

In large-scale network systems, there is a high demand for online optimization, for instance to track time-varying targets in sensor network systems. This article investigates distributed online composite optimization over time-varying, unbalanced multiagent systems with communication delays. Each network node minimizes a local composite objective, consisting of a time-varying convex cost and a nonnegative regularization term. Using bandit feedback, we introduce a distributed online composite push-sum dual averaging algorithm tailored for communication delays. Through rigorous theoretical analysis, we establish an expected time-average regret bound, proving that the algorithm converges with respect to the time horizon $T$ , even under the presence of communication delays. We also explicitly characterize the nontrivial effect of communication delays on the convergence rate. Finally, simulations on the distributed online regularized sensor network optimization problem corroborate our theoretical findings, demonstrating the algorithm's practical efficacy with communication delays.