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arXiv 2503.09497cs.LG
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用于定位的联邦平滑ADMM

Federated Smoothing ADMM for Localization

Norwegian University of Science and Technology(挪威科技大学);Keio University(庆应义塾大学)

Reza Mirzaeifard, Ashkan Moradi, Masahiro Yukawa, Stefan Werner

AI总结:

本文提出一种联邦平滑ADMM定位算法,通过ℓ1范数、总变差平滑近似和Moreau包络处理非凸非光滑问题,支持异步与多客户端更新,在收敛速度和抗异常值方面优于现有方法。

摘要:

本文解决了联邦场景中定位的挑战,该场景具有分布式数据、非凸性和非光滑性的特点。为了解决此类环境中固有的可扩展性和异常值问题,我们提出了一种鲁棒算法,该算法在一种新颖的联邦ADMM框架内采用$\ell_1$范数公式。该方法通过为总变差一致性项集成迭代平滑近似,并对以相减形式出现的凸函数采用Moreau包络近似来解决该问题。这种变换确保了问题在每次迭代中都是光滑且弱凸的,从而提高了计算效率并改善了估计精度。所提出的算法支持异步更新和每次迭代多次客户端更新,这确保了其对现实世界联邦系统的适应性。为了验证所提出算法的可靠性,我们证明了该方法收敛到平稳点,并且数值模拟突显了与现有最先进的定位方法相比,其在收敛速度和异常值恢复能力方面的优越性能。

英文摘要:

This paper addresses the challenge of localization in federated settings, which are characterized by distributed data, non-convexity, and non-smoothness. To tackle the scalability and outlier issues inherent in such environments, we propose a robust algorithm that employs an $\ell_1$-norm formulation within a novel federated ADMM framework. This approach addresses the problem by integrating an iterative smooth approximation for the total variation consensus term and employing a Moreau envelope approximation for the convex function that appears in a subtracted form. This transformation ensures that the problem is smooth and weakly convex in each iteration, which results in enhanced computational efficiency and improved estimation accuracy. The proposed algorithm supports asynchronous updates and multiple client updates per iteration, which ensures its adaptability to real-world federated systems. To validate the reliability of the proposed algorithm, we show that the method converges to a stationary point, and numerical simulations highlight its superior performance in convergence speed and outlier resilience compared to existing state-of-the-art localization methods.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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