Stochastic Event-Triggered Algorithm for Distributed Convex Optimization

This article investigates the problem of distributed convex optimization under constrained communication. A novel stochastic event-triggering algorithm is shown to solve the problem asymptotically to any arbitrarily small error without exhibiting Zeno behavior. A systematic design of the stochastic event processes is then derived from the analysis on the optimality and communication rate with the help of a meta-optimization problem. Finally, a numerical example on distributed classification is provided to visualize the performance of the proposed algorithm in terms of convergence in optimization error and average communication rate with comparison to other algorithms in the literature. We show that the proposed algorithm is highly effective in reducing communication rates compared with algorithms proposed in the literature.