From clinical development of cancer therapies to investigations into partisan bias, adaptive sequential designs have become increasingly popular method for causal inference, as they offer the possibility of improved precision over their non-adaptive counterparts. However, even in simple settings (e.g. two treatments) the extent to which adaptive designs can improve precision is not sufficiently well understood. In this work, we study the problem of Adaptive Neyman Allocation in a design-based potential outcomes framework, where the experimenter seeks to construct an adaptive design which is nearly as efficient as the optimal (but infeasible) non-adaptive Neyman design, which has access to all potential outcomes. Motivated by connections to online optimization, we propose Neyman Ratio and Neyman Regret as two (equivalent) performance measures of adaptive designs for this problem. We present Clip-OGD, an adaptive design which achieves $\widetilde{O}(\sqrt{T})$ expected Neyman regret and thereby recovers the optimal Neyman variance in large samples. Finally, we construct a conservative variance estimator which facilitates the development of asymptotically valid confidence intervals. To complement our theoretical results, we conduct simulations using data from a microeconomic experiment.

翻译：从癌症疗法的临床开发到党派偏见的研究，自适应序贯设计因其相较于非自适应设计能提高统计精度的潜力，已成为因果推断中日益流行的工具。然而，即使在简单场景（如两种处理）中，自适应设计对精度的提升程度尚未得到充分理解。本文在基于设计的潜在结果框架下研究自适应奈曼分配问题：实验者试图构建一种自适应设计，使其效率尽可能接近最优但不可行的非自适应奈曼设计（该设计可访问所有潜在结果）。受在线优化相关研究的启发，我们提出奈曼比率和奈曼遗憾作为该问题下自适应设计的两种（等价的）性能度量。我们提出的Clip-OGD自适应设计可实现$\widetilde{O}(\sqrt{T})$的期望奈曼遗憾，从而在大样本中恢复最优奈曼方差。最后，我们构造了一个保守的方差估计量，为渐进有效置信区间的建立提供支持。为补充理论结果，我们利用微观经济实验数据进行了仿真分析。