Robust support vector machines via conic optimization
This work addresses robustness in machine learning for applications sensitive to outliers, but it is incremental as it builds on existing methods with a focus on computational improvements.
The paper tackles the problem of making support vector machines robust to data perturbations and outliers by developing a new loss function that better approximates the 0-1 loss while preserving convexity. The proposed estimator is competitive with standard SVMs in outlier-free settings and performs better when outliers are present.
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.