Robust support vector machines via conic optimization
Valentina Cepeda Andrés Gómez Shaoning Han
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.