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C-Learner: Constrained Learning for Causal Inference and Semiparametric Statistics

Popular debiased causal estimation methods, e.g. for the average treatment effect -- such as one-step estimation (e.g., augmented inverse propensity weighting) and targeted maximum likelihood estimation -- enjoy desirable asymptotic properties such as statistical efficiency and double robustness. However, they often produce unstable estimates when there is limited overlap between treatment and control, and require ad hoc adjustments in practice (e.g., truncating propensity scores). In contrast, simple plug-in estimators are stable but lack good asymptotic properties. We propose a novel debiased estimator that achieves the best of both worlds, producing stable plug-in estimates with desirable asymptotic properties. Our constrained learning framework solves for the best plug-in estimator under the constraint that the first-order error with respect to the plugged-in quantity is zero, and can leverage flexible model classes including neural networks and tree ensembles. In several experimental settings, including ones in which we handle text-based covariates by fine-tuning language models, our constrained learning-based estimator outperforms one-step estimation and targeting in challenging settings with limited overlap between treatment and control, and performs comparably otherwise.

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