# Quadratic Convergence of Smoothing Newton's Method for 0/1 Loss Optimization

arXiv: https://arxiv.org/abs/2103.14987 · HTML: https://mlsanity.com/paper/2103.14987/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2021.

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

- [0/1 Deep Neural Networks via Block Coordinate Descent](https://mlsanity.com/paper/2206.09379/) (2022)
- [MKL-L0/1-SVM](https://mlsanity.com/paper/2308.12016/) (2023)
- [Local Duality for Sparse Support Vector Machines](https://mlsanity.com/paper/2601.20170/) (2026)

## Abstract (arXiv)

It has been widely recognized that the 0/1 loss function is one of the most natural choices for modelling classification errors, and it has a wide range of applications including support vector machines and 1-bit compressed sensing. Due to the combinatorial nature of the 0/1 loss function, methods based on convex relaxations or smoothing approximations have dominated the existing research and are often able to provide approximate solutions of good quality. However, those methods are not optimizing the 0/1 loss function directly and hence no optimality has been established for the original problem. This paper aims to study the optimality conditions of the 0/1 function minimization, and for the first time to develop Newton's method that directly optimizes the 0/1 function with a local quadratic convergence under reasonable conditions. Extensive numerical experiments demonstrate its superior performance as one would expect from Newton-type methods.ions. Extensive numerical experiments demonstrate its superior performance as one would expect from Newton-type methods.