Robustness and Regularization of Support Vector Machines

We consider regularized support vector machines (SVMs) and show that they are precisely equivalent to a new robust optimization formulation. We show that this equivalence of robust optimization and regularization has implications for both algorithms, and analysis. In terms of algorithms, the equivalence suggests more general SVM-like algorithms for classification that explicitly build in protection to noise, and at the same time control overfitting. On the analysis front, the equivalence of robustness and regularization provides a robust optimization interpretation for the success of regularized SVMs. We use this new robustness interpretation of SVMs to give a new proof of consistency of (kernelized) SVMs, thus establishing robustness as the reason regularized SVMs generalize well.