面向分层网络的通信高效ADMM算法

中文摘要 AI 辅助

本文提出了一种基于交替方向乘子法（ADMM）的新型分布式优化算法，用于解决树形结构网络上的分层优化问题，称为分层ADMM（hADMM），特别关注提升网络中的通信效率。通过重新排列增广拉格朗日函数，在节点间建立一种查询-响应通信机制，该机制显式利用了分层树结构，与现有基于ADMM的分层优化方法相比，所提算法显著降低了通信成本。此外，hADMM在凸性假设下保证了渐近收敛。我们还基于线性矩阵不等式给出了收敛速率分析，以刻画不同网络拓扑下理论上可达到的最大收敛速率，表明所提出的hADMM在温和条件下可实现线性收敛。三个数值实验证明，hADMM兼容任意树形网络结构，并在通信效率方面优于现有方法。

英文摘要

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.

发表机构

• University of Central Florida（中佛罗里达大学）
• Louisiana State University（路易斯安那州立大学）

机构由 AI 辅助整理，请以论文原文为准。