Proximal gradient method for huberized support vector machine

TL;DR

This paper introduces a proximal gradient method for efficiently solving the differentiable Huberized SVM, providing convergence guarantees and demonstrating superior performance over existing methods in classification tasks.

Contribution

It develops a novel proximal gradient algorithm for Huberized SVMs, including multi-class extension, with proven linear convergence and acceleration techniques.

Findings

Algorithm converges linearly under strong convexity.

Finite support convergence results enable acceleration.

Numerical experiments show superior performance over state-of-the-art methods.

Abstract

The Support Vector Machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized SVMs, such as with $\ell_1$-regularization. This paper considers the Huberized SVM (HSVM), which uses a differentiable approximation of the hinge loss function. We first explore the use of the Proximal Gradient (PG) method to solving binary-class HSVM (B-HSVM) and then generalize it to multi-class HSVM (M-HSVM). Under strong convexity assumptions, we show that our algorithm converges linearly. In addition, we give a finite convergence result about the support of the solution, based on which we further accelerate the algorithm by a two-stage method. We present extensive numerical experiments on both synthetic and real datasets which demonstrate the superiority of our methods over some state-of-the-art methods for both binary- and multi-class SVMs.