Learning with convex constraints

In this paper, we focus on multitask learning and discuss the notion of learning from constraints, in which they limit the space of admissible real values of the task functions. We formulate learning as a variational problem and analyze convex constraints, with special attention to the case of linear bilateral and unilateral constraints. Interestingly, we show that the solution is not always an analytic function and that it cannot be expressed by the classic kernel expansion on the training examples. We provide exact and approximate solutions and report experimental evidence of the improvement with respect to classic kernel machines.