Constrained Learning for Causal Inference and Semiparametric Statistics

Causal estimation (e.g. of the average treatment effect) requires estimating complex nuisance parameters (e.g. outcome models). To adjust for errors in nuisance parameter estimation, we present a novel correction method that solves for the best plug-in estimator under the constraint that the first-order error of the estimator with respect to the nuisance parameter estimate is zero. Our constrained learning framework provides a unifying perspective to prominent first-order correction approaches including debiasing (a.k.a. augmented inverse probability weighting) and targeting (a.k.a. targeted maximum likelihood estimation). Our semiparametric inference approach, which we call the "C-Learner", can be implemented with modern machine learning methods such as neural networks and tree ensembles, and enjoys standard guarantees like semiparametric efficiency and double robustness. Empirically, we demonstrate our approach on several datasets, including those with text features that require fine-tuning language models. We observe the C-Learner matches or outperforms other asymptotically optimal estimators, with better performance in settings with less estimated overlap.