  Estimating heterogeneous treatment effects from observational data is a
crucial task across many fields, helping policy and decision-makers take better
actions. There has been recent progress on robust and efficient methods for
estimating the conditional average treatment effect (CATE) function, but these
methods often do not take into account the risk of hidden confounding, which
could arbitrarily and unknowingly bias any causal estimate based on
observational data. We propose a meta-learner called the B-Learner, which can
efficiently learn sharp bounds on the CATE function under limits on the level
of hidden confounding. We derive the B-Learner by adapting recent results for
sharp and valid bounds of the average treatment effect (Dorn et al., 2021) into
the framework given by Kallus & Oprescu (2023) for robust and model-agnostic
learning of conditional distributional treatment effects. The B-Learner can use
any function estimator such as random forests and deep neural networks, and we
prove its estimates are valid, sharp, efficient, and have a quasi-oracle
property with respect to the constituent estimators under more general
conditions than existing methods. Semi-synthetic experimental comparisons
validate the theoretical findings, and we use real-world data to demonstrate
how the method might be used in practice.
