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：我们考虑在存在非平稳性、单元间（空间）干扰和持久效应（时间干扰）情况下的实验设计，旨在估计全局平均处理效应（GATE），即所有单元在所有时刻均接受处理或对照时平均结果之差。假设空间干扰由图结构描述，其中单元的结果依赖于其邻域的处理分配；时间干扰则由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。我们提出一种聚集式开关实验设计，将单元划分为簇，时间步划分为块，并为每个完整的簇-块组合分配单一随机处理。在此设计下，我们证明：对于可良好聚类的图，截断暴露映射霍维茨-汤普森估计量能够实现均方误差（MSE）的$\tilde O(1/NT)$量级，匹配$\Omega(1/NT)$下界（至多差对数项）。我们的结果同时推广了Hu和Wager（2022）中$N=1$的设置（并改进了其中针对差分均值估计量所证明的MSE界），以及Ugander等人（2013）和Leung（2022）中$T=1$的设置。仿真实验验证了所提方法的优越性能。