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.

翻译：因果估计（例如平均处理效应的估计）通常需要估计复杂的干扰参数（例如结果模型）。为了调整干扰参数估计中的误差，我们提出了一种新颖的修正方法，该方法在保证估计量相对于干扰参数估计的一阶误差为零的约束条件下，求解最优的插件估计量。我们的约束学习框架为包括去偏（也称为增广逆概率加权）和针对性估计（也称为针对性最大似然估计）在内的一阶修正方法提供了统一的视角。我们提出的半参数推断方法称为“C-Learner”，可借助现代机器学习方法（如神经网络和树集成）实现，并享有半参数效率与双重稳健性等标准保证。在实证中，我们使用多个数据集展示了该方法，包括需要微调语言模型的文本特征数据集。我们观察到C-Learner与其他渐近最优估计器性能相当或更优，且在估计重叠度较低的情况下表现更好。