Abstract: As a new margin-based classifier, -learning shows great potential for high accuracy. However, the optimization of -learning involves non-convex minimization and is very challenging to implement. In this article, we convert the optimization of -learning into a mixed integer programming (MIP) problem. This enables us to utilize the state-of-art algorithm of MIP to solve -learning. Moreover, the new algorithm can solve -learning with a general piecewise linear loss and does not require continuity of the loss function. We also examine the variable selection property of 1-norm -learning and make comparisons with the SVM.
Key words and phrases: Classification, norm, regularization, SVM, variable selection.