Improving Convergence Rate of Distributed Consensus Through Asymmetric Weights

TL;DR

This paper introduces a novel asymmetric weight design method that significantly enhances the convergence rate of distributed consensus algorithms, outperforming symmetric and traditional weight schemes, especially in large or complex networks.

Contribution

It develops a new asymmetric weight design approach that improves convergence rates and uses continuum approximation for general graphs, surpassing existing symmetric methods.

Findings

Asymmetric weights improve convergence rate significantly.

Convergence rate can be independent of graph size with proper weights.

Numerical results outperform symmetric and Metropolis-Hastings weights.

Abstract

We propose a weight design method to increase the convergence rate of distributed consensus. Prior work has focused on symmetric weight design due to computational tractability. We show that with proper choice of asymmetric weights, the convergence rate can be improved significantly over even the symmetric optimal design. In particular, we prove that the convergence rate in a lattice graph can be made independent of the size of the graph with asymmetric weights. We then use a Sturm-Liouville operator to approximate the graph Laplacian of more general graphs. A general weight design method is proposed based on this continuum approximation. Numerical computations show that the resulting convergence rate with asymmetric weight design is improved considerably over that with symmetric optimal weights and Metropolis-Hastings weights.