We consider experimentation in the presence of non-stationarity, inter-unit (spatial) interference, and carry-over effects (temporal interference), where we wish to estimate the global average treatment effect (GATE), the difference between average outcomes having exposed all units at all times to treatment or to control. We suppose spatial interference is described by a graph, where a unit's outcome depends on its neighborhood's treatment assignments, and that temporal interference is described by a hidden Markov decision process, where the transition kernel under either treatment (action) satisfies a rapid mixing condition. We propose a clustered switchback design, where units are grouped into clusters and time steps are grouped into blocks and each whole cluster-block combination is assigned a single random treatment. Under this design, we show that for graphs that admit good clustering, a truncated exposure-mapping Horvitz-Thompson estimator achieves $\tilde O(1/NT)$ mean-squared error (MSE), matching an $\Omega(1/NT)$ lower bound up to logarithmic terms. Our results simultaneously generalize the $N=1$ setting of Hu, Wager 2022 (and improves on the MSE bound shown therein for difference-in-means estimators) as well as the $T=1$ settings of Ugander et al 2013 and Leung 2022. Simulation studies validate the favorable performance of our approach.

翻译：我们考虑在非平稳性、单元间（空间）干扰和遗留效应（时间干扰）存在下的实验设计，旨在估计全局平均处理效应（GATE），即所有单元在所有时间点均接受处理或均接受控制时的平均结果差异。我们假设空间干扰由一张图描述，其中单元的结果取决于其邻域的处理分配；时间干扰则由一个隐马尔可夫决策过程描述，其中任一处理（动作）下的转移核满足快速混合条件。我们提出一种聚类切换设计：将单元分组为聚类，将时间步分组为区块，每个完整的聚类-区块组合被随机分配单一处理。在此设计下，我们证明对于允许良好聚类的图，基于截断暴露映射的霍维茨-汤普森估计量可实现$\tilde O(1/NT)$均方误差（MSE），该结果与$\Omega(1/NT)$下界仅相差对数项。我们的结果同时推广了Hu与Wager（2022）中$N=1$的情境（并改进了其中针对均值差分估计量所展示的MSE界），以及Ugander等人（2013）和Leung（2022）中$T=1$的情境。模拟研究验证了我们方法的优越性能。