Dynamic Regret and Cumulative Constraint Violation Analysis for Distributed Online Constrained Convex Optimization with Event-Triggered Communication

This paper focuses on the distributed online convex optimization problem with time-varying inequality constraints over a network of agents, where each agent collaborates with its neighboring agents to minimize the cumulative network-wide loss over time. To reduce communication overhead between the agents, we propose a distributed event-triggered online primal-dual algorithm over a time-varying directed graph. Dynamic network regret and network cumulative constraint violation are leveraged to measure the performance of the algorithm. Based on the natural decreasing parameter sequences, we establish sublinear dynamic network regret and network cumulative constraint violation bounds. The theoretical results broaden the applicability of event-triggered online convex optimization to the regime with inequality constraints. Finally, a numerical simulation example is provided to verify the theoretical results.