  This paper proposes a unified framework for the investigation of constrained
learning theory in reflexive Banach spaces of features via regularized
empirical risk minimization. The focus is placed on Tikhonov-like
regularization with totally convex functions. This broad class of regularizers
provides a flexible model for various priors on the features, including in
particular hard constraints and powers of Banach norms. In such context, the
main results establish a new general form of the representer theorem and the
consistency of the corresponding learning schemes under general conditions on
the loss function, the geometry of the feature space, and the modulus of total
convexity of the regularizer. In addition, the proposed analysis gives new
insight into basic tools such as reproducing Banach spaces, feature maps, and
universality. Even when specialized to Hilbert spaces, this framework yields
new results that extend the state of the art.
