Distributed Online Optimization with Edge-Based Event-Triggered communication

Shuai Mao, Yateendra Mishra, Yu-Chu Tian, Matjaz Perc, Yang Tang

Abstract: 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<math><mi mathvariant="script" is="true">B</mi></math>-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)<math><mrow is="true"><mi mathvariant="script" is="true">O</mi><mrow is="true"><mo is="true">(</mo><msup is="true"><mrow is="true"><mrow is="true"><mo is="true">(</mo><mo class="qopname" is="true">ln</mo><mrow is="true"><mo is="true">(</mo><mi is="true">T</mi><mo is="true">)</mo></mrow><mo is="true">)</mo></mrow></mrow><mrow is="true"><mn is="true">2</mn></mrow></msup><mo is="true">)</mo></mrow></mrow></math> and O(T)<math><mrow is="true"><mi mathvariant="script" is="true">O</mi><mrow is="true"><mo is="true">(</mo><msqrt is="true"><mrow is="true"><mi is="true">T</mi></mrow></msqrt><mo is="true">)</mo></mrow></mrow></math>, respectively. Simulation results in time-varying economic dispatch and online prediction for diabetes validate the efficacy of the proposed EBET-DOO.