Enhanced multi-task learning using optimization methods

This paper presents an improved multi-task twin support vector machine method utilizing Universum data, referred to as I-UMTSVM. A significant advancement of I-UMTSVM over UMTSVM is the addition of a regularization term, which facilitates the application of the structural risk minimization principle. This modification captures the essence of statistical learning theory and leads to enhanced classification performance. Two approaches are proposed for solving the I-UMTSVM problem. The first is a dual formulation of I-UMTSVM, which involves solving a quadratic programming problem. The second, NI-UMTSVM, is a Newton-based approach that addresses I-UMTSVM in the primal space. In NI-UMTSVM, the constrained optimization problems of I-UMTSVM are transformed into unconstrained ones, and a generalized Newton’s method is introduced to solve them effectively. The efficiency of the proposed methods is demonstrated through numerical experiments on various benchmark multi-task data sets. These experiments provide evidence of the effectiveness and strong performance of the proposed approaches in multi-task learning tasks.