Iterative regularization in classification via hinge loss diagonal descent

TL;DR

This paper introduces an iterative regularization method for classification using hinge loss and diagonal descent, providing convergence guarantees and stability analysis, with promising numerical results.

Contribution

It develops a novel diagonal descent-based iterative regularization approach for classification with theoretical convergence and stability guarantees.

Findings

Proves convergence and rates for the proposed method.

Demonstrates stability under classification noise.

Shows favorable performance in numerical simulations.

Abstract

Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical accuracy. On the other hand it allows to shed light on the learning curves observed while training neural networks. In this paper, we focus on iterative regularization in the context of classification. After contrasting this setting with that of linear inverse problems, we develop an iterative regularization approach based on the use of the hinge loss function. More precisely we consider a diagonal approach for a family of algorithms for which we prove convergence as well as rates of convergence and stability results for a suitable classification noise model. Our approach compares favorably with other alternatives, as confirmed by numerical simulations.