  In this contribution we apply an adaptive model hierarchy, consisting of a
full-order model, a reduced basis reduced order model, and a machine learning
surrogate, to parametrized linear-quadratic optimal control problems. The
involved reduced order models are constructed adaptively and are called in such
a way that the model hierarchy returns an approximate solution of given
accuracy for every parameter value. At the same time, the fastest model of the
hierarchy is evaluated whenever possible and slower models are only queried if
the faster ones are not sufficiently accurate. The performance of the model
hierarchy is studied for a parametrized heat equation example with boundary
value control.
