Optimizing Ψ-learning via Mixed Integer Programming

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