A constrained machine-learning paradigm

The classical framework of learning from examples is enhanced by the introduction of hard pointwise constraints, i.e., constraints imposed on a finite set of examples that cannot be violated. Such constraints arise, e.g., when requiring coherent decisions of classifiers acting on different views of the same pattern. It is shown that the optimal solution to the learning problem with hard bilateral and linear pointwise constraints can be obtained as the limit of the sequence of optimal solutions to the related learning problems with soft bilateral and linear pointwise constraints, when the penalty parameter tends to infinity. Numerical examples are presented, where hard linear pointwise constraints combined with soft pointwise constraints induced by supervised examples.