Federated Smoothing ADMM for Localization

2025-03-12

AI Summary

Federated learning for localization faces challenges including data heterogeneity, nonconvex and nonsmooth objective functions, sensitivity to outliers, and poor scalability. Method: This paper proposes a robust federated ADMM algorithm. It is the first to integrate ℓ₁-norm-based robust modeling with a smoothed ADMM framework; introduces a smooth approximation of the iterative total variation consensus term; and employs the Moreau envelope to handle subtraction-type nonconvex terms, ensuring each subproblem is weakly convex and solvable per iteration. The algorithm supports asynchronous updates and concurrent participation of multiple clients. Contribution/Results: We establish theoretical convergence to a stationary point under standard assumptions. Empirical evaluations demonstrate faster convergence and significantly improved robustness against outliers compared to state-of-the-art methods.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Computer Vision: Adversarial Attacks & Robustness
• Search and Optimization: Local Search

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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.

Problem

• Addresses localization in federated settings with distributed data.
• Proposes a robust algorithm for scalability and outlier issues.
• Ensures smooth and weakly convex iterations for efficiency.

Innovation

• Uses $ell_1$-norm in federated ADMM framework
• Integrates smooth approximation for total variation
• Employs Moreau envelope for convex function smoothing