Distributed Maximum Consensus over Noisy Links

TL;DR

This work tackles distributed maximum consensus over noisy communication links by reformulating the problem as a distributed optimization and solving it with ADMM. The proposed RD-MC algorithm introduces two robustness enhancements: exchanging a smoothed signal $s_i(k)=2\bar{x}_i(k)-x_i(k)$ using a single noisy estimate set, and applying a sliding-window average $\bar{x}_i(k{+}1)=\sum_{\ell=0}^{\mathcal{C}-1} \alpha_{\ell} x_i(k{+}1-\ell)$ to suppress noise, with neighbor messages $\tilde{s}_j(k)=s_j(k)+w_i^j(k)$. The method yields updates for $x_i$, $y_i$, $\bar{u}_i$, $z_i$, and $s_i$ that converge to the network maximum $a^\star=\max_i a_i$ with bounded error, outperforming naive max-consensus and the prior D-MC in simulations on networks with varying connectivity and noise levels. Overall, RD-MC provides robust, scalable distributed maximum consensus in realistically noisy networks, with practical impact for decentralized decision-making under unreliable communications.

Abstract

We introduce a distributed algorithm, termed noise-robust distributed maximum consensus (RD-MC), for estimating the maximum value within a multi-agent network in the presence of noisy communication links. Our approach entails redefining the maximum consensus problem as a distributed optimization problem, allowing a solution using the alternating direction method of multipliers. Unlike existing algorithms that rely on multiple sets of noise-corrupted estimates, RD-MC employs a single set, enhancing both robustness and efficiency. To further mitigate the effects of link noise and improve robustness, we apply moving averaging to the local estimates. Through extensive simulations, we demonstrate that RD-MC is significantly more robust to communication link noise compared to existing maximum-consensus algorithms.

Figures (7)

• Figure 1: The considered network with an arbitrary topology and $J = 20$ agents.
• Figure 2: The impact of noise on the performance of naive-MC \ref{['eq:convmaxcons']}, D-MC algorithm \ref{['eq:FDUp']} and RD-MC algorithm \ref{['eq:FDRobust']} with window size $\mathcal{C} = 3$ and noise variance $\sigma^2 = 0.1$.
• Figure 3: The effect of noise variance on the steady-state network-wide MSE of RD-MC with window size $\mathcal{C} = 1$ and different noise variances $\sigma^2 \in \{ 0.0001, 0.01, 0.1\}$.
• Figure 4: The effect of noise variance on the steady-state network-wide MSE of RD-MC with window size $\mathcal{C} = 2$ and different noise variances $\sigma^2 \in \{ 0.001, 0.01, 0.1\}$.
• Figure 5: The effect of noise variance on the steady-state network-wide MSE of RD-MC with window size $\mathcal{C} = 3$ and different noise variances $\sigma^2 \in \{ 0.001, 0.01, 0.1\}$.