Generalized R-learner for Estimating Potential Outcome and Treatment Effects

Estimating potential outcome and treatment effects from observation data is important for decision making. Orthogonal learners represent a growing area of research that develops target estimators insensitive to plug-in nuisance functions. Among existing orthogonal learners, the R-learner offers an approach that is free from numerical instability due to inverse propensities, yet it is derived based on partially linear outcome equations. We develop a *target-error* analysis for the R-learner to isolate an explicit *structural-drift* term that represents the gap between class-optimal plug-in target and the oracle target, revealing that the partially linear structure leads to a structural-drift *not reducible by the target estimator.* We accordingly present a generalized R-learner (GRL) that is able to accommodate this structural drift by utilizing a general nonlinear outcome equation in the target estimator, and provide an orthogonality regularized objective function that serves the dual purpose of reducing nuisance-induced structural drift in the target estimator while providing a nuisance-robust population risk bound. We establish conditions under which GRL achieves smaller target errors and when the target remains resolvable under nuisance estimation errors. On (semi-)synthetic and real datasets, we empirically demonstrated the strength of GRL in comparison to existing meta-learners in both potential outcome and treatment effect estimation.