# Robust support vector machines via conic optimization

arXiv: https://arxiv.org/abs/2402.01797 · HTML: https://mlsanity.com/paper/2402.01797/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 13 of 13)

- [Making Risk Minimization Tolerant to Label Noise](https://mlsanity.com/paper/1403.3610/) (2014)
- [Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimization](https://mlsanity.com/paper/2004.06152/) (2020)
- [Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitions](https://mlsanity.com/paper/1709.10029/) (2017)
- [Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approach](https://mlsanity.com/paper/2109.12701/) (2021)
- [Regularization vs. Relaxation: A conic optimization perspective of statistical variable selection](https://mlsanity.com/paper/1510.06083/) (2015)
- [Rank-one Convexification for Sparse Regression](https://mlsanity.com/paper/1901.10334/) (2019)
- [Mixed-Projection Conic Optimization: A New Paradigm for Modeling Rank Constraints](https://mlsanity.com/paper/2009.10395/) (2020)
- [Exact and Approximation Algorithms for Sparse PCA](https://mlsanity.com/paper/2008.12438/) (2020)
- [Solving sparse principal component analysis with global support](https://mlsanity.com/paper/2010.11152/) (2020)
- [Safe Screening Rules for ℓ0-Regression](https://mlsanity.com/paper/2004.08773/) (2020)
- [The ratio-cut polytope and K-means clustering](https://mlsanity.com/paper/2006.15225/) (2020)
- [On the convex hull of convex quadratic optimization problems with indicators](https://mlsanity.com/paper/2201.00387/) (2022)
- [Supersparse Linear Integer Models for Predictive Scoring Systems](https://mlsanity.com/paper/1306.5860/) (2013)

## Abstract (arXiv)

We consider the problem of learning support vector machines robust to uncertainty. It has been established in the literature that typical loss functions, including the hinge loss, are sensible to data perturbations and outliers, thus performing poorly in the setting considered. In contrast, using the 0-1 loss or a suitable non-convex approximation results in robust estimators, at the expense of large computational costs. In this paper we use mixed-integer optimization techniques to derive a new loss function that better approximates the 0-1 loss compared with existing alternatives, while preserving the convexity of the learning problem. In our computational results, we show that the proposed estimator is competitive with the standard SVMs with the hinge loss in outlier-free regimes and better in the presence of outliers.