Distributed Online Mirror Descent With Delayed Subgradient and Event-Triggered Communications

This paper investigates the distributed online multi-agent convex-constrained optimization with limited network bandwidth and feedback delay. The distinctive feature is that each agent is associated with a loss function that changes over time. It is desirable to employ an event-triggered communication protocol during the information exchange process to conserve network resources. Then, by adopting the Bregman divergence, we propose a delayed-subgradient-based event-triggered online distributed mirror descent (DS-ET-ODMD) algorithm that operates under delayed-full-information feedback. Under the DS-ET-ODMD algorithmic framework, we establish upper bounds for both static and dynamic regret of each agent, ensuring that the growth of such regrets is sublinear with respect to the time horizon
$T$
as the trigger threshold gradually approaches zero. Finally, we provide distributed online estimation and target tracking problems as the simulation examples to verify our proposed algorithm.