The design of experiments involves a compromise between covariate balance and robustness. This paper provides a formalization of this trade-off and describes an experimental design that allows experimenters to navigate it. The design is specified by a robustness parameter that bounds the worst-case mean squared error of an estimator of the average treatment effect. Subject to the experimenter's desired level of robustness, the design aims to simultaneously balance all linear functions of potentially many covariates. Less robustness allows for more balance. We show that the mean squared error of the estimator is bounded in finite samples by the minimum of the loss function of an implicit ridge regression of the potential outcomes on the covariates. Asymptotically, the design perfectly balances all linear functions of a growing number of covariates with a diminishing reduction in robustness, effectively allowing experimenters to escape the compromise between balance and robustness in large samples. Finally, we describe conditions that ensure asymptotic normality and provide a conservative variance estimator, which facilitate the construction of asymptotically valid confidence intervals.

翻译：实验设计涉及协变量平衡与稳健性之间的权衡。本文对这一权衡进行了形式化描述，并提出了一种可供实验者灵活调节该矛盾的实验设计。该设计通过一个稳健性参数来界定平均处理效应估计量的最坏情况均方误差。在满足实验者期望的稳健性水平前提下，该设计旨在同时平衡多个潜在协变量的所有线性函数。较低的稳健性要求可实现更优的平衡性。我们证明，在有限样本条件下，估计量的均方误差受限于潜在结果对协变量进行隐含岭回归损失函数的最小值。随着协变量数量增加，该设计能渐近完美平衡所有线性函数，同时稳健性的衰减幅度逐渐减小，从而使实验者在大量样本下有效突破平衡性与稳健性之间的权衡困境。最后，我们给出了确保渐近正态性的条件，并提出了保守方差估计量，从而为构建渐近有效置信区间提供了理论支撑。