Lower bound performances for average consensus in open multi-agent systems (extended version)

TL;DR

This paper establishes fundamental lower bounds on the performance of averaging algorithms in open multi-agent systems with dynamic agent populations, highlighting inherent limitations in estimation accuracy.

Contribution

It introduces a theoretical lower bound on mean square error for averaging in systems with random agent arrivals and departures, under pairwise communication constraints.

Findings

Lower bounds on estimation error are derived for open multi-agent systems.

Performance limitations are characterized under random agent dynamics.

The results apply to systems with pairwise, random communication protocols.

Abstract

We derive fundamental limitations on the performances of intrinsic averaging algorithms in open multi-agent systems, which are systems subject to random arrivals and departures of agents. Each agent holds a value, and their goal is to estimate the average of the values of the agents presently in the system. We provide a lower bound on the expected Mean Square Error for any estimation algorithm, assuming that the number of agents remains constant and that communications are random and pairwise. Our derivation is based on the expected error obtained with an optimal algorithm under conditions more favorable than those the actual problem allows, and relies on an analysis of the constraints on the information spreading mechanisms in the system, and relaxations of these.