  Orthogonal meta-learners, such as DR-learner, R-learner and IF-learner, are
increasingly used to estimate conditional average treatment effects. They
improve convergence rates relative to na\"{\i}ve meta-learners (e.g., T-, S-
and X-learner) through de-biasing procedures that involve applying standard
learners to specifically transformed outcome data. This leads them to disregard
the possibly constrained outcome space, which can be particularly problematic
for dichotomous outcomes: these typically get transformed to values that are no
longer constrained to the unit interval, making it difficult for standard
learners to guarantee predictions within the unit interval. To address this, we
construct orthogonal meta-learners for the prediction of counterfactual
outcomes which respect the outcome space. As such, the obtained i-learner or
imputation-learner is more generally expected to outperform existing learners,
even when the outcome is unconstrained, as we confirm empirically in simulation
studies and an analysis of critical care data. Our development also sheds
broader light onto the construction of orthogonal learners for other estimands.
