  In this paper, we introduce a new functional point of view on bilevel
optimization problems for machine learning, where the inner objective is
minimized over a function space. These types of problems are most often solved
by using methods developed in the parametric setting, where the inner objective
is strongly convex with respect to the parameters of the prediction function.
The functional point of view does not rely on this assumption and notably
allows using over-parameterized neural networks as the inner prediction
function. We propose scalable and efficient algorithms for the functional
bilevel optimization problem and illustrate the benefits of our approach on
instrumental regression and reinforcement learning tasks.
