Accelerated Consensus via Min-Sum Splitting

TL;DR

This paper introduces Min-Sum Splitting, a modified message-passing algorithm that accelerates convergence in distributed consensus problems, matching the performance of advanced optimization methods.

Contribution

It demonstrates that Min-Sum Splitting achieves accelerated convergence rates in consensus problems, a significant improvement over the standard Min-Sum algorithm.

Findings

Min-Sum Splitting converges where Min-Sum does not.

Proper tuning yields subdiffusive accelerated rates.

The method aligns with lifted Markov chains and multi-step optimization techniques.

Abstract

We apply the Min-Sum message-passing protocol to solve the consensus problem in distributed optimization. We show that while the ordinary Min-Sum algorithm does not converge, a modified version of it known as Splitting yields convergence to the problem solution. We prove that a proper choice of the tuning parameters allows Min-Sum Splitting to yield subdiffusive accelerated convergence rates, matching the rates obtained by shift-register methods. The acceleration scheme embodied by Min-Sum Splitting for the consensus problem bears similarities with lifted Markov chains techniques and with multi-step first order methods in convex optimization.