Edge-Based Event-Triggered Online Distributed Inexact Gradient Descent Algorithm

This work addresses the challenge of performing distributed online convex optimization in resource-constrained systems, including IoT networks and wireless sensor networks, where communication resources are limited. We develop an edge-based event-triggered (EBET) distributed inexact gradient descent algorithm that departs from the conventional requirement of full state exchange at every iteration. In the proposed scheme, each communication link is equipped with an independent triggering rule; an agent forwards its current estimate to a neighbor only after the state deviation on that link surpasses a user-specified threshold, thereby eliminating redundant transmissions. The algorithm additionally tolerates bounded errors in the gradient evaluation, making it applicable to settings where exact gradients are either unavailable or too costly to compute. Through a Lyapunov-like analysis that couples the consensus update with the non-expansive projection operator, we show that the static regret of every agent grows at a sublinear rate of OT provided that the step size, gradient error bound, and triggering threshold are chosen appropriately. Simulation results on regularized linear regression and logistic regression tasks validate the theoretical findings, confirming that sublinear regret is attained with far fewer communication rounds than a fully connected baseline, thus achieving a favorable balance between solution quality and communication cost.