  We consider parametrized linear-quadratic optimal control problems and
provide their online-efficient solutions by combining greedy reduced basis
methods and machine learning algorithms. To this end, we first extend the
greedy control algorithm, which builds a reduced basis for the manifold of
optimal final time adjoint states, to the setting where the objective
functional consists of a penalty term measuring the deviation from a desired
state and a term describing the control energy. Afterwards, we apply machine
learning surrogates to accelerate the online evaluation of the reduced model.
The error estimates proven for the greedy procedure are further transferred to
the machine learning models and thus allow for efficient a posteriori error
certification. We discuss the computational costs of all considered methods in
detail and show by means of two numerical examples the tremendous potential of
the proposed methodology.
