Distributed Estimation Via a Roaming Token

TL;DR

This paper introduces a distributed estimation algorithm using a roaming token that moves through a network via a Markov chain, achieving asymptotic optimality and outperforming some existing methods.

Contribution

It proposes a novel roaming token algorithm for distributed estimation that is proven to be consistent and asymptotically optimal under various network conditions.

Findings

Algorithm is consistent and asymptotically optimal.

Achieves smaller MSE than consensus+innovations algorithms in simulations.

Performs well in both i.i.d. and deterministic network scenarios.

Abstract

We present an algorithm for the problem of linear distributed estimation of a parameter in a network where a set of agents are successively taking measurements. The approach considers a roaming token in a network that carries the estimate, and jumps from one agent to another in its vicinity according to the probabilities of a Markov chain. When the token is at an agent it records the agent's local information. We analyze the proposed algorithm and show that it is consistent and asymptotically optimal, in the sense that its mean-square-error (MSE) rate of decay approaches the centralized one as the number of iterations increases. We show these results for a scenario where the network changes over time, and we consider two different set of assumptions on the network instantiations: they are i.i.d. and connected on the average, or they are deterministic and strongly connected for every finite time window of a fixed size. Simulations show our algorithm is competitive with consensus+innovations type algorithms, achieving a smaller MSE at each iteration in all considered scenarios.