The X-Learner

Estimating how much a treatment (a marketing offer, a drug, a trading signal flag) changes an outcome for each individual is harder than estimating an average effect, because you only ever observe one outcome per person, either treated or not, never both. Meta-learners solve this by turning the problem into a sequence of ordinary supervised-learning fits. The X-Learner is one such recipe, designed specifically to handle unbalanced groups, such as when only 5% of customers received a promotion.

It works in stages. First, fit separate outcome models on the treated group and the control group. Second, use each model to impute the "missing" counterfactual outcome for the other group, predicting what a treated person's outcome would have looked like untreated, and vice versa, and compute the resulting individual-level effect estimates. Third, fit two more models to smooth those imputed effects, one trained on each group, and combine them using a weighting function (often the propensity score) that leans more heavily on whichever group's estimate is more reliable.

Worked example

A retailer sent a discount coupon to only 8% of its customer base. An S-Learner or T-Learner would struggle because the control-group model is trained on far more data than the treatment-group model, biasing effect estimates toward whichever group the underlying model was more confident about. The X-Learner instead uses the well-trained control model to impute what treated customers would have done untreated, produces a treatment-effect estimate from the small treated group, weights it against the control-side estimate by propensity score, and ends up less distorted by the size imbalance.