We consider two new formulations for classification problems in the spirit of support vector machines based on robust optimization. Our formulations are designed to build in protection to noise and control overfitting, but without being overly conservative. Our first formulation allows the noise between different samples to be correlated. We show that the standard norm-regularized support vector machine classifier is a solution to a special case of our first formulation, thus providing an explicit link between regularization and robustness in pattern classification. Our second formulation is based on a softer version of robust optimization called comprehensive robustness. We show that this formulation is equivalent to regularization by any arbitrary convex regularizer, thus extending our first equivalence result. Moreover, we explain how the connection of comprehensive robustness to convex risk-measures can be used to design risk-measure constrained classifiers with robustness to the input distribution. Our formulations result in convex optimization problems that can be easily solved. Finally, we provide some empirical results that show the promise of comprehensive robust classifiers.

本文将正则化支持向量机与鲁棒优化公式进行比较，并表明它们是精确等效的。这个比较对算法和分析有影响，可以构建出保护噪声和同时控制过拟合的分类问题的更一般的类 SVM 算法，同时提供正则化 SVM 成功率鲁棒优化解释的分析证明，从而明确了鲁棒性是正则化 SVM 泛化良好的原因。

支持向量机的鲁棒性与正则化