  This paper presents a framework for inverse learning of objective functions
for constrained optimal control problems, which is based on the
Karush-Kuhn-Tucker (KKT) conditions. We discuss three variants corresponding to
different model assumptions and computational complexities. The first method
uses a convex relaxation of the KKT conditions and serves as the benchmark. The
main contribution of this paper is the proposition of two learning methods that
combine the KKT conditions with maximum likelihood estimation. The key benefit
of this combination is the systematic treatment of constraints for learning
from noisy data with a branch-and-bound algorithm using likelihood arguments.
This paper discusses theoretic properties of the learning methods and presents
simulation results that highlight the advantages of using the maximum
likelihood formulation for learning objective functions.
