论文标题
自适应A/B测试和同时处理参数优化
Adaptive A/B Tests and Simultaneous Treatment Parameter Optimization
论文作者
论文摘要
通过有效的中央限制定理构建渐近有效的置信区间对于A/B测试至关重要，在该测试中，经典目标是统计地断言治疗计划是否明显优于控制计划。在某些在线平台的新兴应用程序中，治疗计划不是一个计划，而是包含一个无限的计划，该计划由连续的治疗参数索引。因此，实验者不仅需要提供有效的统计推断，而且还希望有效和适应地找到用于治疗计划的治疗参数的最佳价值选择。但是，我们发现，尽管经典优化算法在凸度假设下具有快速的收敛速率，但并未带有可用于构建渐近有效置信区间的中心极限定理。我们通过提供一种新的优化算法来解决此问题，该算法一方面保持相同的快速收敛率，另一方面允许建立有效的中央限制定理。我们讨论了所提出的算法的实际实现，并进行数值实验以说明理论发现。
Constructing asymptotically valid confidence intervals through a valid central limit theorem is crucial for A/B tests, where a classical goal is to statistically assert whether a treatment plan is significantly better than a control plan. In some emerging applications for online platforms, the treatment plan is not a single plan, but instead encompasses an infinite continuum of plans indexed by a continuous treatment parameter. As such, the experimenter not only needs to provide valid statistical inference, but also desires to effectively and adaptively find the optimal choice of value for the treatment parameter to use for the treatment plan. However, we find that classical optimization algorithms, despite of their fast convergence rates under convexity assumptions, do not come with a central limit theorem that can be used to construct asymptotically valid confidence intervals. We fix this issue by providing a new optimization algorithm that on one hand maintains the same fast convergence rate and on the other hand permits the establishment of a valid central limit theorem. We discuss practical implementations of the proposed algorithm and conduct numerical experiments to illustrate the theoretical findings.
