  Machine learning has witnessed tremendous success in solving tasks depending
on a single hyperparameter. When considering simultaneously a finite number of
tasks, multi-task learning enables one to account for the similarities of the
tasks via appropriate regularizers. A step further consists of learning a
continuum of tasks for various loss functions. A promising approach, called
\emph{Parametric Task Learning}, has paved the way in the continuum setting for
affine models and piecewise-linear loss functions. In this work, we introduce a
novel approach called \emph{Infinite Task Learning} whose goal is to learn a
function whose output is a function over the hyperparameter space. We leverage
tools from operator-valued kernels and the associated vector-valued RKHSs that
provide an explicit control over the role of the hyperparameters, and also
allows us to consider new type of constraints. We provide generalization
guarantees to the suggested scheme and illustrate its efficiency in
cost-sensitive classification, quantile regression and density level set
estimation.
