Average treatment effect estimation is the most central problem in causal
inference with application to numerous disciplines. While many estimation
strategies have been proposed in the literature, recently also incorporating
generic machine learning estimators, the statistical optimality of these
methods has still remained an open area of investigation. In this paper, we
adopt the recently introduced structure-agnostic framework of statistical lower
bounds, which poses no structural properties on the nuisance functions other
than access to black-box estimators that attain small errors; which is
particularly appealing when one is only willing to consider estimation
strategies that use non-parametric regression and classification oracles as a
black-box sub-process. Within this framework, we prove the statistical
optimality of the celebrated and widely used doubly robust estimators for both
the Average Treatment Effect (ATE) and the Average Treatment Effect on the
Treated (ATTE), as well as weighted variants of the former, which arise in
policy evaluation.

在这篇论文中，我们采用最近引入的无结构统计下界框架，证明了双重稳健估计器在平均处理效应以及对待处理群体的平均处理效应方面的统计优越性，以及这些估计器的加权变体，这在政策评估中广泛应用。

双重补偿学习在治疗效果估计中的无结构优化性

Structure-agnostic Optimality of Doubly Robust Learning for Treatment  Effect Estimation

While random forests are commonly used for regression problems, existing
methods often lack adaptability in complex situations or lose optimality under
simple, smooth scenarios. In this study, we introduce the adaptive split
balancing forest (ASBF), capable of learning tree representations from data
while simultaneously achieving minimax optimality under the Lipschitz class. To
exploit higher-order smoothness levels, we further propose a localized version
that attains the minimax rate under the H\"older class $\mathcal{H}^{q,\beta}$
for any $q\in\mathbb{N}$ and $\beta\in(0,1]$. Rather than relying on the
widely-used random feature selection, we consider a balanced modification to
existing approaches. Our results indicate that an over-reliance on auxiliary
randomness may compromise the approximation power of tree models, leading to
suboptimal results. Conversely, a less random, more balanced approach
demonstrates optimality. Additionally, we establish uniform upper bounds and
explore the application of random forests in average treatment effect
estimation problems. Through simulation studies and real-data applications, we
demonstrate the superior empirical performance of the proposed methods over
existing random forests.

本研究介绍了自适应分割平衡森林（ASBF）方法，能够在同时达到 Lipschitz 类的极小极值优化和 H"older 类的极小速率优化的条件下，从数据中学习树的表示。通过平衡修改现有方法，我们进一步提出了一种局部化版本来利用更高阶的平滑水平。实验结果表明，过度依赖辅助随机性可能会损害树模型的逼近能力，导致次优结果。相反，一种不那么随机、更加平衡的方法表现出最佳性。此外，我们还确定了均匀上界，并探讨了随机森林在平均处理效应估计问题中的应用。通过模拟研究和实际数据应用，我们展示了所提出方法相对于现有随机森林的卓越实证表现。