I study the minimax‐optimal design for a two‐arm controlled experiment where conditional mean outcomes vary in a given set and the objective is effect‐estimation precision. When this set is permutation symmetric, the optimal design is shown to be complete randomization. Notably, even when the set has structure (i.e., is not permutation symmetric), being minimax‐optimal for precision still requires randomization beyond a single partition of units, that is, beyond randomizing the identity of treatment. A single partition is not optimal even when conditional means are linear. Since this only targets precision, it may nonetheless not ensure sufficient uniformity for design‐based (i.e., randomization) inference. I therefore propose the inference‐constrained mixed‐strategy optimal design as the minimax‐optimal for precision among designs subject to sufficient‐uniformity constraints.

中文翻译：

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关于实验设计中随机化的最优性：如何针对最小最大方差和基于设计的推理进行随机化

我研究了两臂控制实验的最小最大最优设计，在该实验中，条件均值在给定集合中有所不同，并且目标是效果估计精度。当此集合是置换对称的时，最佳设计显示为完全随机。值得注意的是，即使集合具有结构（即，不是排列对称的），为达到精度而使minimax最优，仍然需要对单元的单个分区以外的区域进行随机化，即对治疗的身份进行随机化。即使条件均值是线性的，单个分区也不是最优的。由于这仅以精度为目标，因此仍然可能无法确保基于设计的推理（即随机化）具有足够的一致性。