Experiments are the gold standard for causal inference. In many applications, experimental units can often be recruited or chosen sequentially, and the adaptive execution of such experiments may offer greatly improved inference of causal quantities over non-adaptive approaches, particularly when experiments are expensive. We thus propose a novel active learning method called ACE (Active learning for Causal inference with Expensive experiments), which leverages Gaussian process modeling of the conditional mean functions to guide an informed sequential design of costly experiments. In particular, we develop new acquisition functions for sequential design via the minimization of the posterior variance of a desired causal estimand. Our approach facilitates targeted learning of a variety of causal estimands, such as the average treatment effect (ATE), the average treatment effect on the treated (ATTE), and individualized treatment effects (ITE), and can be used for adaptive selection of an experimental unit and/or the applied treatment. We then demonstrate in a suite of numerical experiments the improved performance of ACE over baseline methods for estimating causal estimands given a limited number of experiments.

翻译：实验是因果推断的黄金标准。在许多应用中，实验单元通常可以顺序招募或选择，而此类实验的自适应执行相较于非自适应方法，能够大幅提升因果量的推断效率，尤其是在实验成本高昂的场景下。为此，我们提出一种新型主动学习方法——ACE（面向昂贵实验的因果推断主动学习），该方法利用条件均值函数的高斯过程建模，指导昂贵实验的知情序贯设计。具体而言，我们通过最小化目标因果估计量的后验方差，开发出用于序贯设计的新采集函数。我们的方法可促进多种因果估计量的定向学习，例如平均处理效应（ATE）、处理组平均处理效应（ATTE）及个体处理效应（ITE），并能用于实验单元和/或施予处理的自适应选择。通过一系列数值实验，我们证明在实验数量有限的情况下，ACE方法在因果估计量估计方面相较于基线方法具有更优性能。