🤖 AI Summary
This paper addresses the challenge of unbiased estimation of the global average treatment effect (GATE) in online experiments subject to spatial interference (cross-unit spillovers), temporal carryover effects (lagged treatment impacts), and nonstationarity (time-varying potential outcomes). To tackle these issues, we propose the first causal inference framework integrating graph clustering with a block-switching experimental design: graph clustering captures the underlying spatial dependence structure; a Markov decision process models dynamic treatment allocation over time; and a truncated Horvitz–Thompson estimator corrects for both spatial and temporal interference. We establish that the mean squared error (MSE) of our estimator converges at rate Õ(1/(NT)), matching the information-theoretic lower bound for sparse graphs. Simulation results demonstrate substantial improvements in estimation accuracy over conventional switching designs.
📝 Abstract
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 treatments, and that temporal interference is described by an MDP, 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 Horvitz-Thompson estimator achieves a $ ilde O(1/NT)$ mean squared error (MSE), matching the lower bound up to logarithmic terms for sparse graphs. Our results simultaneously generalize the results from citet{hu2022switchback,ugander2013graph} and citet{leung2022rate}. Simulation studies validate the favorable performance of our approach.
