We study the design and analysis of switchback experiments conducted on a
single aggregate unit. The design problem is to partition the continuous time
space into intervals and switch treatments between intervals, in order to
minimize the estimation error of the treatment effect. We show that the
estimation error depends on four factors: carryover effects, periodicity,
serially correlated outcomes, and impacts from simultaneous experiments. We
derive a rigorous bias-variance decomposition and show the tradeoffs of the
estimation error from these factors. The decomposition provides three new
insights in choosing a design: First, balancing the periodicity between treated
and control intervals reduces the variance; second, switching less frequently
reduces the bias from carryover effects while increasing the variance from
correlated outcomes, and vice versa; third, randomizing interval start and end
points reduces both bias and variance from simultaneous experiments. Combining
these insights, we propose a new empirical Bayes design approach. This approach
uses prior data and experiments for designing future experiments. We illustrate
this approach using real data from a ride-sharing platform, yielding a design
that reduces MSE by 33% compared to the status quo design used on the platform.

我们研究在单个聚合单元上进行的回溯实验的设计和分析问题，推导出了误差估计依赖于交叉效应、周期性、序列相关的结果以及同步实验的影响等四个因素，并提出了三个新的设计见解，最后提出了一种基于经验贝叶斯的设计方法，并在实际数据的基础上进行了验证。