Communication-efficient ADMM over Hierarchical Networks
Abstract
This paper develops a novel distributed optimization algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve hierarchical optimization problems over tree-structured networks, termed hierarchical ADMM (hADMM), with a particular focus on enhancing communication efficiency across the network. By rearranging the augmented Lagrangian to establish a query-response communication mechanism between nodes that explicitly exploits the hierarchical tree structure, the proposed algorithm significantly reduces communication costs compared to existing ADMM-based methods for hierarchical optimization. Furthermore, hADMM guarantees asymptotic convergence under convexity assumptions. We also present a convergence rate analysis based on linear matrix inequalities to characterize the maximum theoretically achievable convergence rates across different network topologies, showing that the proposed hADMM attains linear convergence under mild conditions. Three numerical experiments demonstrate that hADMM is compatible with arbitrary tree network structures and outperforms existing approaches in terms of communication efficiency.
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BibTeX
@misc{nguyen2026communicationefficient,
title = {{Communication-efficient ADMM over Hierarchical Networks}},
author = {Binh Nguyen and Shuangqing Wei and Truong X. Nghiem},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09361},
eprint = {2609.09361},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09361},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Communication-efficient ADMM over Hierarchical Networks
AU - Binh Nguyen
AU - Shuangqing Wei
AU - Truong X. Nghiem
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.09361
UR - https://arxiv.org/abs/2609.09361
AB - This paper develops a novel distributed optimization algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve hierarchical optimization problems over tree-structured networks, termed hierarchical ADMM (hADMM), with a particular focus on enhancing communication efficiency across the network. By rearranging the augmented Lagrangian to establish a query-response communication mechanism between nodes that explicitly exploits the hierarchical tree structure, the proposed algorithm significantly reduces communication costs compared to existing ADMM-based methods for hierarchical optimization. Furthermore, hADMM guarantees asymptotic convergence under convexity assumptions. We also present a convergence rate analysis based on linear matrix inequalities to characterize the maximum theoretically achievable convergence rates across different network topologies, showing that the proposed hADMM attains linear convergence under mild conditions. Three numerical experiments demonstrate that hADMM is compatible with arbitrary tree network structures and outperforms existing approaches in terms of communication efficiency.
ER -