  Motivated by applications in personalized medicine and individualized
policymaking, there is a growing interest in techniques for quantifying
treatment effect heterogeneity in terms of the conditional average treatment
effect (CATE). Some of the most prominent methods for CATE estimation developed
in recent years are T-Learner, DR-Learner and R-Learner. The latter two were
designed to improve on the former by being Neyman-orthogonal. However, the
relations between them remain unclear, and likewise the literature remains
vague on whether these learners converge to a useful quantity or (functional)
estimand when the underlying optimization procedure is restricted to a class of
functions that does not include the CATE. In this article, we provide insight
into these questions by discussing DR-Learner and R-Learner as special cases of
a general class of weighted Neyman-orthogonal learners for the CATE, for which
we moreover derive oracle bounds. Our results shed light on how one may
construct Neyman-orthogonal learners with desirable properties, on when
DR-Learner may be preferred over R-Learner (and vice versa), and on novel
learners that may sometimes be preferable to either of these. Theoretical
findings are confirmed using results from simulation studies on synthetic data,
as well as an application in critical care medicine.
