Event-triggered Broadcasting for Distributed Smooth Optimization

This work addresses a class of distributed optimization problems where the global objective function is the sum of multiple local convex smooth functions privately held by a group of working agents. Upon modeling the unconstrained distributed optimization problem as a linearly constrained centralized one, a communication-efficient event-triggered first-order primal-dual algorithm that only requires light local computation at each generic time instant and peer-to-peer communication at sporadic triggering time instants is developed to solve the global problem. An O\left( {\frac{1}{k}} \right) convergence rate is ensured, provided that the stepsize satisfies a condition that relates to the Lipschitz constant of the gradient and the Laplacian of the communication graph, and the time-varying triggering threshold is monotonically decreasing and summable. The proposed method is applied to a decentralized logistic regression problem to illustrate its effectiveness, especially in saving communication resources.