Distributionally robust chance constrained svm model with $\ell_2$-Wasserstein distance

Abstract

<p style='text-indent:20px;'>In this paper, we propose a distributionally robust chance-constrained SVM model with <inline-formula><tex-math id="M1">\begin{document}$ \ell_2 $\end{document}</tex-math></inline-formula>-Wasserstein ambiguity. We present equivalent formulations of distributionally robust chance constraints based on <inline-formula><tex-math id="M2">\begin{document}$ \ell_2 $\end{document}</tex-math></inline-formula>-Wasserstein ambiguity. In terms of this method, the distributionally robust chance-constrained SVM model can be transformed into a solvable linear 0-1 mixed integer programming problem when the <inline-formula><tex-math id="M3">\begin{document}$ \ell_2 $\end{document}</tex-math></inline-formula>-Wasserstein distance is discrete form. The DRCC-SVM model could be transformed into a tractable 0-1 mixed-integer SOCP programming problem for the continuous case. Finally, numerical experiments are given to illustrate the effectiveness and feasibility of our model.</p>