Minimizing Type 2 Errors in an Experiment-Rich Regime via Optimal Resource Allocation
实验密集环境下通过最优资源配置降低第二类错误AI 解读 ↓
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实验密集环境下通过最优资源配置降低第二类错误
- 研究问题
- 多项随机实验同时争夺有限资源时，如何配置样本以降低最坏情形的第二类错误，而不仅关注治疗效应估计的均方误差？
- 方法与思路
- 作者先刻画已知标准差下的功效最优配置，再用校正因子膨胀先导方差估计，构造不同风险准则的优化框架和可计算替代程序。
- 材料陈述的贡献
- 摘要称直接代入先导标准差可能损失功效，提出的 Surrogate-S 仅使用先导方差估计，并在数值实验中达到接近已知参数基准的表现。
- 阅读关注点
- 应核对实质效应阈值、最坏情形的定义、先导样本如何分配，以及校正因子、风险准则与替代优化的理论保证如何对应。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未说明检验与资源约束的具体条件，近基准表现仅由所述数值实验支持。
原文摘要
Randomized experiments (often known as "A/B tests") are widely used to evaluate product and service innovations. We study how to allocate limited experimentation resources across M concurrent experiments in an experiment-rich regime. Existing work on allocation has predominantly focused on minimizing the worst-case mean squared error (MSE) of estimated treatment effects, which favors experiments with larger (and typically unknown) outcome variance. While appropriate for controlling estimation accuracy, this objective does not directly capture a common managerial priority in screening stages: detecting practically meaningful treatment effects with high probability. Motivated by this, we consider the objective of minimizing the worst-case Type II error across all experiments. When the standard deviations are known, we characterize the power-optimal allocation and show that MSE-based allocations can be highly inefficient for detection, even though the two objectives align asymptotically. When the standard deviations are unknown and must be learned from pilot data, we show that a naive plug-in approach, treating pilot standard deviations as truth, can suffer substantial power loss. We propose inflating pilot estimates via correction factors and develop three optimization-based frameworks for selecting them, each reflecting a different risk criterion with distinct managerial implications. Although the resulting stochastic programs are computationally challenging at scale, we derive tractable surrogate reformulations inspired by robust optimization and establish favorable theoretical properties. We further propose Surrogate-S, a fully data-dependent and implementable procedure that computes correction factors using only pilot variance estimates and achieves near-oracle performance in numerical experiments.