Conditional average treatment effect (CATE) estimation is the de facto gold standard for targeting a treatment to a heterogeneous population. The method estimates treatment effects up to an error $ε> 0$ in each of $M$ different strata of the population, targeting individuals in decreasing order of estimated treatment effect until the budget runs out. In general, this method requires $O(M/ε^2)$ samples. This is best possible if the goal is to estimate all treatment effects up to an $ε$ error. In this work, we show how to achieve the same total treatment effect as CATE with only $O(M/ε)$ samples for natural distributions of treatment effects. The key insight is that coarse estimates suffice for near-optimal treatment allocations. In addition, we show that budget flexibility can further reduce the sample complexity of allocation. Finally, we evaluate our algorithm on various real-world RCT datasets. In all cases, it finds nearly optimal treatment allocations with surprisingly few samples. Our work highlights the fundamental distinction between treatment effect estimation and treatment allocation: the latter requires far fewer samples.

翻译：条件平均处理效应（CATE）估计是面向异质人群进行干预定向的事实黄金标准。该方法通过估计人群$M$个不同分层中每个分层的处理效应，误差控制在$ε> 0$以内，并按照估计处理效应从高到低的顺序定向个体直至预算耗尽。一般而言，该方法需要$O(M/ε^2)$样本量。若目标是将所有处理效应估计误差控制在$ε$以内，这已达到理论最优。本研究表明，对于处理效应的自然分布，仅需$O(M/ε)$样本量即可实现与CATE相同的总处理效应。关键发现在于：粗糙估计足以实现接近最优的干预分配。此外，我们证明预算灵活性可进一步降低分配任务的样本复杂度。最后，我们在多个真实世界随机对照试验数据集上评估所提算法。在所有案例中，该算法均能以极少的样本量找到接近最优的干预分配方案。本研究揭示了处理效应估计与干预分配之间的本质区别：后者所需的样本量远少于前者。