# Bias of Homotopic Gradient Descent for the Hinge Loss

arXiv: https://arxiv.org/abs/1907.11746 · HTML: https://mlsanity.com/paper/1907.11746/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2019.

## Built on by (most cited first, 3 of 3)

- [Classification of Data Generated by Gaussian Mixture Models Using Deep ReLU Networks](https://mlsanity.com/paper/2308.08030/) (2023)
- [Iterative regularization in classification via hinge loss diagonal descent](https://mlsanity.com/paper/2212.12675/) (2022)
- [Bridging Unsupervised and Semi-Supervised Anomaly Detection: A Theoretically-Grounded and Practical Framework with Synthetic Anomalies](https://mlsanity.com/paper/2506.13955/) (2025)

## Abstract (arXiv)

Gradient descent is a simple and widely used optimization method for machine learning. For homogeneous linear classifiers applied to separable data, gradient descent has been shown to converge to the maximal margin (or equivalently, the minimal norm) solution for various smooth loss functions. The previous theory does not, however, apply to non-smooth functions such as the hinge loss which is widely used in practice. Here, we study the convergence of a homotopic variant of gradient descent applied to the hinge loss and provide explicit convergence rates to the max-margin solution for linearly separable data.