  Learn-to-Defer is a paradigm that enables learning algorithms to work not in
isolation but as a team with human experts. In this paradigm, we permit the
system to defer a subset of its tasks to the expert. Although there are
currently systems that follow this paradigm and are designed to optimize the
accuracy of the final human-AI team, the general methodology for developing
such systems under a set of constraints (e.g., algorithmic fairness, expert
intervention budget, defer of anomaly, etc.) remains largely unexplored. In
this paper, using a $d$-dimensional generalization to the fundamental lemma of
Neyman and Pearson (d-GNP), we obtain the Bayes optimal solution for
learn-to-defer systems under various constraints. Furthermore, we design a
generalizable algorithm to estimate that solution and apply this algorithm to
the COMPAS and ACSIncome datasets. Our algorithm shows improvements in terms of
constraint violation over a set of baselines.
