Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Federated Smoothing ADMM for Localization

Reza Mirzaeifard, Ashkan Moradi, Masahiro Yukawa, Stefan Werner

TL;DR

This work tackles robust localization in federated settings where data are distributed and prone to outliers. It introduces a federated ADMM approach that uses an $L1$-norm objective together with smoothing-based total variation consensus and a Moreau-envelope approximation to keep subproblems smooth and weakly convex, enabling asynchronous, multi-update optimization. The authors provide convergence guarantees to a stationary point and show via simulations that the method achieves faster convergence and improved outlier resilience compared with state-of-the-art methods like DSLR. The proposed approach is well-suited for IoT and cyber-physical systems requiring privacy-preserving, scalable, and robust localized inference in heterogeneous environments.

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.

Federated Smoothing ADMM for Localization

TL;DR

This work tackles robust localization in federated settings where data are distributed and prone to outliers. It introduces a federated ADMM approach that uses an -norm objective together with smoothing-based total variation consensus and a Moreau-envelope approximation to keep subproblems smooth and weakly convex, enabling asynchronous, multi-update optimization. The authors provide convergence guarantees to a stationary point and show via simulations that the method achieves faster convergence and improved outlier resilience compared with state-of-the-art methods like DSLR. The proposed approach is well-suited for IoT and cyber-physical systems requiring privacy-preserving, scalable, and robust localized inference in heterogeneous environments.

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 -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.

Paper Structure

This paper contains 5 sections, 1 theorem, 28 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Distributed Robust Localization
  4. Simulation Results
  5. Conclusion

Key Result

Theorem 1

Assume that the parameters $\mu_{\xi}^{(k_l)}$, $\mu_{h}^{(k_l)}$, $\sigma_{\phi}^{(k_l)}$ and $\sigma_{\psi}^{(k_l)}$ are updated according to eq:up:sm, $\beta d \geq \sqrt{80}$ and $\alpha c \geq \sqrt{\frac{3}{2}}$. Then, Algorithm alg:1 converges to a stationary point $\left(\{\mathbf{x}_l^{*}, where $\boldsymbol{\zeta}_l^{*} = -\boldsymbol{\xi}_l^{*}$ for each $l \in \{1,\cdots,L\}$.

Figures (3)

  • Figure 1: RMSE versus outlier probability.
  • Figure 2: RMSE versus scale parameter of Cauchy noise.
  • Figure 3: RMSE versus iterations.

Theorems & Definitions (1)

  • Theorem 1: Global Convergence