  Efficiently and flexibly estimating treatment effect heterogeneity is an
important task in a wide variety of settings ranging from medicine to
marketing, and there are a considerable number of promising conditional average
treatment effect estimators currently available. These, however, typically rely
on the assumption that the measured covariates are enough to justify
conditional exchangeability. We propose the P-learner, motivated by the R- and
DR-learner, a tailored two-stage loss function for learning heterogeneous
treatment effects in settings where exchangeability given observed covariates
is an implausible assumption, and we wish to rely on proxy variables for causal
inference. Our proposed estimator can be implemented by off-the-shelf
loss-minimizing machine learning methods, which in the case of kernel
regression satisfies an oracle bound on the estimated error as long as the
nuisance components are estimated reasonably well.
