A machine-learning paradigm that includes pointwise constraints

The classical framework of learning from examples is enhanced by the introduction of hard point-wise constraints, i.e., constraints, on a finite set of examples, that cannot be violated. They arise, e.g., when imposing coherent decisions of classifiers acting on different views of the same pattern. Constrained variational calculus is exploited to derive a representer theorem that provides a description of the functional structure of the solution. The general theory is applied to learning from hard linear point-wise constraints combined with classical supervised pairs and loss functions.