  We present a study of surrogate losses and algorithms for the general problem
of learning to defer with multiple experts. We first introduce a new family of
surrogate losses specifically tailored for the multiple-expert setting, where
the prediction and deferral functions are learned simultaneously. We then prove
that these surrogate losses benefit from strong $H$-consistency bounds. We
illustrate the application of our analysis through several examples of
practical surrogate losses, for which we give explicit guarantees. These loss
functions readily lead to the design of new learning to defer algorithms based
on their minimization. While the main focus of this work is a theoretical
analysis, we also report the results of several experiments on SVHN and
CIFAR-10 datasets.
