# Efficient Distributed Learning over Decentralized Networks with Convoluted Support Vector Machine

arXiv: https://arxiv.org/abs/2503.07563 · HTML: https://mlsanity.com/paper/2503.07563/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 68 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates](https://mlsanity.com/paper/1704.07807/) (2017)
- [Communication-Efficient Accurate Statistical Estimation](https://mlsanity.com/paper/1906.04870/) (2019)
- [Smoothed Quantile Regression with Large-Scale Inference](https://mlsanity.com/paper/2012.05187/) (2020)
- [Multi-Agent Distributed Optimization via Inexact Consensus ADMM](https://mlsanity.com/paper/1402.6065/) (2014)
- [Quantile Regression Under Memory Constraint](https://mlsanity.com/paper/1810.08264/) (2018)
- [Smoothing quantile regressions](https://mlsanity.com/paper/1905.08535/) (2019)
- [High-Dimensional Quantile Regression: Convolution Smoothing and Concave Regularization](https://mlsanity.com/paper/2109.05640/) (2021)
- [Distributed Inference for Linear Support Vector Machine](https://mlsanity.com/paper/1811.11922/) (2018)
- [Distributed Discrete-time Optimization in Multi-agent Networks Using only Sign of Relative State](https://mlsanity.com/paper/1709.08360/) (2017)
- [A Distributed and Integrated Method of Moments for High-Dimensional Correlated Data Analysis](https://mlsanity.com/paper/1910.02986/) (2019)
- [Fast and Robust Sparsity Learning over Networks: A Decentralized Surrogate Median Regression Approach](https://mlsanity.com/paper/2202.05498/) (2022)
- [Empirical Likelihood Inference over Decentralized Networks](https://mlsanity.com/paper/2401.12836/) (2024)

## Abstract (arXiv)

This paper addresses the problem of efficiently classifying high-dimensional data over decentralized networks. Penalized support vector machines (SVMs) are widely used for high-dimensional classification tasks. However, the double nonsmoothness of the objective function poses significant challenges in developing efficient decentralized learning methods. Many existing procedures suffer from slow, sublinear convergence rates. To overcome this limitation, we consider a convolution-based smoothing technique for the nonsmooth hinge loss function. The resulting loss function remains convex and smooth. We then develop an efficient generalized alternating direction method of multipliers (ADMM) algorithm for solving penalized SVM over decentralized networks. Our theoretical contributions are twofold. First, we establish that our generalized ADMM algorithm achieves provable linear convergence with a simple implementation. Second, after a sufficient number of ADMM iterations, the final sparse estimator attains near-optimal statistical convergence and accurately recovers the true support of the underlying parameters. Extensive numerical experiments on both simulated and real-world datasets validate our theoretical findings.