Firms increasingly use randomized experiments to decide whether to scale up an intervention and, if so, how to re-optimize related operational choices such as inventory, capacity, or pricing. In many settings, experiments are performed on small samples, so the estimated effect of the intervention is uncertain. A common practice is to plug a 'significant' estimate of the effect into both (i) the rollout rule and (ii) the downstream optimization. However, this can lead to avoidable losses because the costs of over- versus under-estimating the effect are often asymmetric. The technically ideal approach is to obtain a data-dependent decision rule that minimizes the Bayes risk, but this lacks transparency and requires more computations. We propose Predict-Adjust-Then-Rollout-Optimize (PATRO), a plug-in approach that keeps the standard estimate, but makes data-independent adjustments, respectively, for the two types of decision. We show that the two adjustments can be substitutes or complements and provide an alternating-iteration method to compute the pair. PATRO performs both in theory and numerically close or equivalent to the Bayes-optimal benchmark, making it a simple, effective way to convert noisy experimental results into better rollout and operational decisions.

翻译：企业越来越多地采用随机实验来决定是否扩大干预措施的实施规模，并在决定推广时，如何重新优化相关的运营选择，如库存、产能或定价。在许多场景中，实验基于小样本进行，因此干预效果的估计存在不确定性。常见的做法是将一个“显著”的效果估计值同时代入（i）推广规则和（ii）下游优化中。然而，这种做法可能导致可避免的损失，因为高估与低估效果的成本通常是不对称的。技术上的理想方法是获得一个数据依赖的决策规则，以最小化贝叶斯风险，但这缺乏透明度且需要更多计算。我们提出了预测-调整-然后推广-优化（Predict-Adjust-Then-Rollout-Optimize, PATRO），这是一种插件方法，它保留了标准的估计值，但针对两种决策类型分别进行数据独立的调整。我们证明了这两种调整可以是替代或互补关系，并提供了一种交替迭代方法来计算这对调整量。PATRO在理论和数值上均表现接近或等同于贝叶斯最优基准，使其成为一种将嘈杂的实验结果转化为更优推广与运营决策的简单有效方法。