  In this paper, we propose an approach for learning sparse reject option
classifiers using double ramp loss $L_{dr}$. We use DC programming to find the
risk minimizer. The algorithm solves a sequence of linear programs to learn the
reject option classifier. We show that the loss $L_{dr}$ is Fisher consistent.
We also show that the excess risk of loss $L_d$ is upper bounded by the excess
risk of $L_{dr}$. We derive the generalization error bounds for the proposed
approach. We show the effectiveness of the proposed approach by experimenting
it on several real world datasets. The proposed approach not only performs
comparable to the state of the art but it also successfully learns sparse
classifiers.
