  Estimating the conditional average treatment effect (CATE) from observational
data is relevant for many applications such as personalized medicine. Here, we
focus on the widespread setting where the observational data come from multiple
environments, such as different hospitals, physicians, or countries.
Furthermore, we allow for violations of standard causal assumptions, namely,
overlap within the environments and unconfoundedness. To this end, we move away
from point identification and focus on partial identification. Specifically, we
show that current assumptions from the literature on multiple environments
allow us to interpret the environment as an instrumental variable (IV). This
allows us to adapt bounds from the IV literature for partial identification of
CATE by leveraging treatment assignment mechanisms across environments. Then,
we propose different model-agnostic learners (so-called meta-learners) to
estimate the bounds that can be used in combination with arbitrary machine
learning models. We further demonstrate the effectiveness of our meta-learners
across various experiments using both simulated and real-world data. Finally,
we discuss the applicability of our meta-learners to partial identification in
instrumental variable settings, such as randomized controlled trials with
non-compliance.
