This study focuses on Distributed Online Optimization (DOO) problems with and without constraints.

It presents a discrete-time distributed method based on a push-sum protocol with Edge-Based Event-Triggered communications for DOO (EBET-DOO). In EBET-DOO, all agents operate within both unbalanced time-varying B -strongly connected topologies or unbalanced fixed strongly connected topologies due to the push-sum-based operation.

They estimate and update time-varying optimal solutions in real time by using local objective functions and information from neighboring agents. Communication updates are governed by edge-based triggering conditions, reducing communication frequency compared to node-based event-triggered mechanisms.

We demonstrate that, with specific triggered thresholds, EBET-DOO achieves sublinear growth rates for static regret (for both constrained and unconstrained optimization) and dynamic regret (for constrained optimization only), with orders of O ( ( ln ( T ) ) 2 ) and O ( T ) , respectively.

Simulation results in time-varying economic dispatch and online prediction for diabetes validate the efficacy of the proposed EBET-DOO.

S. Mao, Y. Mishra, Y. Tian, M. Perc, Y. Tang, Distributed Online Optimization with Edge-Based Event-Triggered communication, Automatica 173(2025) 112068.