Distributed online constrained convex optimization with edge-based event-triggered communication mechanisms

The implementation of existing distributed online optimization methods typically relies on real-time information exchange between nodes in a communication network, which incurs unsustainable resource consumption such as communication bandwidth in practical applications. To reduce communication costs, edge-based event-triggering technology is applied to distributed online constrained convex optimization, where each agent only knows its own time-varying local objective functions, and the common goal of all agents is to calculate the optimal sequence of solutions to minimize the total network objective value(the sum of all local objective functions). Firstly, an edge-based event-triggering mechanism is designed for the distributed online gradient descent algorithm under the assumption of a fixed strongly connected directed graph. Then, based on the designed edge-based event-triggering mechanism, an upper bound for each agent′s Regret is established, which is found to be directly related to the event-triggering threshold. Further analysis reveals that as long as the edge-based event-triggering threshold converges to zero over time, the Regret exhibits sublinear growth. Finally, the effectiveness of the proposed algorithm is verified through numerical simulation experiments oriented towards time-varying economic dispatch and diabetes classification prediction problems.