喻园管理论坛2021年第40期(总第697期)

演讲主题: Design and Analysis of Switchback Experiments

               回旋实验的设计与分析

主 讲 人: 赵经隆，波士顿大学助理教授

主 持 人: 关   旭，生产运作与物流管理系教授

活动时间: 2021年6月22日（周二）10:00-11:30

活动地点: 线上腾讯会议，会议ID：276 779 814，会议密码：210622

主讲人简介：

赵经隆，本科毕业于清华工业工程系，博士就读于麻省理工学院，现在波士顿大学(Boston University)任职助理教授。其研究方向主要是研究优化和计量经济学之间的接口，利用离散优化技术来解决大数据时代的数字实验设计问题。其研究成果发表在ManagementScience等国际权威期刊上。

活动简介：

In switchback experiments, a firm sequentially exposes an experimental unit to a random treatment, measures its response, and repeats the procedure for several periods to determine which treatment leads to the best outcome. Although practitioners have widely adopted this experimental design technique, the development of its theoretical properties and the derivation of optimal designs have been elusive. In this paper, we establish the necessary results for practitioners to apply this powerful class of experiments with minimal assumptions. Our main result is the derivation of the optimal design of switchback experiments under a range of different assumptions on the order of the carryover effect --- that is, the length of time a treatment persists in impacting the outcome. We cast the optimal experimental design problem as a minimax discrete optimization problem, identify the worst-case adversarial strategy, establish structural results, and solve the reduced problem via a continuous relaxation. For switchback experiments conducted under the optimal design, we provide two approaches for performing inference. The first provides exact randomization based p-values, and the second uses a new finite population central limit theorem to conduct conservative hypothesis tests and build confidence intervals. We further provide theoretical results when the order of the carryover effect is misspecified. For firms that possess the capability to run multiple switchback experiments, we also provide a data-driven procedure to identify the likely order of the carryover effect. We conduct extensive simulations to study the empirical properties of our results, and conclude with some practical suggestions.

在回旋实验中，公司依次将一个实验单元暴露在一个随机处理中，测量它的反应，并重复这个过程几个周期，以确定哪种处理能产生最好的结果。尽管实践者已经广泛采用了这种实验设计技术，但其理论特性的发展和优化设计的推导一直难以捉摸。在本文中，我们为实践者建立必要的结果，以应用这种强大的实验与最小的假设。我们的主要结果是推导出了在一系列不同假设下的回旋实验的最优设计，这些假设是关于遗留效应的顺序的，即一个处理持续影响结果的时间长度。我们将最优试验设计问题转化为极大极小离散优化问题，识别最坏情况对抗策略，建立结构结果，并通过连续松弛求解简化问题。对于在优化设计下进行的回切实验，我们提供了两种执行推理的方法。第一种方法提供了基于p值的精确随机化，第二种方法利用新的有限总体中心极限定理进行保守假设检验并建立置信区间。我们进一步给出了在延迟效应顺序不确定的情况下的理论结果。对于那些有能力运行多个回旋实验的公司，我们还提供了一个数据驱动的程序，以确定遗留效应的可能顺序。我们进行了广泛的模拟来研究我们的结果的经验性质，并得出一些实用的建议。