Dynamic Median Consensus Over Random Networks

TL;DR

This paper introduces a consensus+innovations algorithm with clipped innovations for distributed median estimation over random networks, proving almost sure convergence despite noisy observations and network randomness.

Contribution

It presents a novel distributed median consensus algorithm that converges under noisy, random network conditions, with proven almost sure convergence and sublinear rate.

Findings

Convergence of local estimates to median(s) almost surely

Algorithm effective under noisy observations and random networks

Numerical experiments validate theoretical results

Abstract

This paper studies the problem of finding the median of N distinct numbers distributed across networked agents. Each agent updates its estimate for the median from noisy local observations of one of the N numbers and information from neighbors. We consider an undirected random network that is connected on average, and a noisy observation sequence that has finite variance and almost surely decaying bias. We present a consensus+innovations algorithm with clipped innovations. Under some regularity assumptions on the network and observation model, we show that each agent's local estimate converges to the set of median(s) almost surely at an asymptotic sublinear rate. Numerical experiments demonstrate the effectiveness of the presented algorithm.