Event-Triggered Distributed Nonconvex Optimization with Progress-Based Threshold

This work studies the distributed nonconvex optimization problem in bandwidth-limited communication environments. We develop a communication-efficient algorithm based on the gradient-tracking based distributed optimization method, where each computation node is equipped with a new event-triggered communication scheduler. Such scheduler approves the broadcasting only when the innovation of exchanged variables exceeds the change of decision variables in two consecutive updates. Compared to the conventional scheduler with time-dependent vanishing thresholds, the proposed one adapts better to the optimization dynamics and thus leads to more significant communication reduction. Finally, we prove the convergence of the algorithm and illustrate its performance via numerical examples.