Exact Average Consensus under Noisy Communication Links: A Decentralized Gradient Perspective
Abstract
We study the distributed average consensus problem under persistent link-level disturbances modeled as a martingale difference sequence with uniformly bounded conditional second moments. Under such disturbances, the standard stochastic-approximation-based linear iteration with diminishing stepsizes drives the network to consensus on an unbiased random variable with non-vanishing variance instead of the exact initial average. To understand and resolve this limitation, we develop an anchoring-based mechanism derived from a decentralized gradient descent formulation and study the effect of incorporating a decaying anchoring term that continuously pulls each agent state toward its initial value. This perspective provides an intuitive interpretation of how state anchoring counteracts disturbance accumulation. Under standard summability conditions, we prove that the resulting algorithm achieves exact average consensus almost surely. Furthermore, this decentralized gradient perspective offers a unifying framework for several related methods and an interpretable design principle for exact average consensus under persistent disturbances.
Related
- Budget-Constrained Multi-Consensus Decentralized Gradient Descent
- Accelerated Consensus and Decentralized Optimization over Slowly Varying Networks
- Stochastic consensus dynamics for decentralized decision systems
- Average Energy Dissipation Rates of Implicit-Explicit Runge-Kutta Methods for Gradient Flow Problems
- Composite and Stochastic Smoothed Decentralized Bregman Proximal-Gradient Methods
BibTeX
@misc{deng2026exact,
title = {{Exact Average Consensus under Noisy Communication Links: A Decentralized Gradient Perspective}},
author = {Yuhang Deng and Zheng Chen and Erik G. Larsson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28082},
eprint = {2609.28082},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28082},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Exact Average Consensus under Noisy Communication Links: A Decentralized Gradient Perspective
AU - Yuhang Deng
AU - Zheng Chen
AU - Erik G. Larsson
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28082
UR - https://arxiv.org/abs/2609.28082
AB - We study the distributed average consensus problem under persistent link-level disturbances modeled as a martingale difference sequence with uniformly bounded conditional second moments. Under such disturbances, the standard stochastic-approximation-based linear iteration with diminishing stepsizes drives the network to consensus on an unbiased random variable with non-vanishing variance instead of the exact initial average. To understand and resolve this limitation, we develop an anchoring-based mechanism derived from a decentralized gradient descent formulation and study the effect of incorporating a decaying anchoring term that continuously pulls each agent state toward its initial value. This perspective provides an intuitive interpretation of how state anchoring counteracts disturbance accumulation. Under standard summability conditions, we prove that the resulting algorithm achieves exact average consensus almost surely. Furthermore, this decentralized gradient perspective offers a unifying framework for several related methods and an interpretable design principle for exact average consensus under persistent disturbances.
ER -