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.

翻译：我们研究了在不确定性条件下学习鲁棒支持向量机的问题。已有文献表明，典型的损失函数（包括铰链损失）对数据扰动和异常值敏感，因此在所考虑的场景中性能较差。相比之下，使用0-1损失或合适的非凸近似虽然能获得鲁棒估计器，但计算成本高昂。本文采用混合整数优化技术推导出一种新的损失函数，该函数比现有替代方案更好地逼近0-1损失，同时保持学习问题的凸性。计算结果表明，所提出的估计器在无异常值场景下与标准铰链损失支持向量机性能相当，而在存在异常值时表现更优。