Tackling heavy-tailed noise in distributed estimation: Asymptotic performance and tradeoffs

2026-03-21

AI Summary

This work addresses the challenge of heavy-tailed noise severely degrading accuracy and stability in distributed parameter estimation within densely deployed systems such as the Internet of Things. The authors propose a robust distributed estimation algorithm grounded in a nonlinear consensus+innovations framework, incorporating general nonlinear functions in both consensus and innovation updates to mitigate the adverse effects of heavy-tailed noise. For the first time under heavy-tailed noise conditions, the paper establishes theoretical guarantees of almost sure convergence and asymptotic normality for the proposed algorithm, revealing a quantitative trade-off between noise decay rates and network connectivity. The method achieves both estimation consistency and asymptotic optimality, thereby providing a novel theoretical foundation for highly robust distributed learning.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We present an algorithm for distributed estimation of an unknown vector parameter $\boldsymbolθ^\ast \in {\mathbb R}^M$ in the presence of heavy-tailed observation and communication noises. Heavy-tailed noises frequently appear, e.g., in densely deployed Internet of Things (IoT) or wireless sensor network systems. The presented algorithm falls within the class of \emph{consensus+innovation} estimators and combats the effect of the heavy-tailed noises by adding general nonlinearities in the consensus and innovations update parts. We present results on almost sure convergence and asymptotic normality of the estimator. In addition, we provide novel analytical studies that reveal interesting tradeoffs between the system noises and the underlying network topology.

Problem

• heavy-tailed noise
• distributed estimation
• consensus+innovation
• asymptotic performance
• network topology

Innovation

• heavy-tailed noise
• distributed estimation
• consensus+innovation
• nonlinear updates
• asymptotic normality