Clustered Switchback Designs for Experimentation Under Spatio-temporal Interference

TL;DR

This paper introduces a clustered switchback experimental design to accurately estimate global effects in complex spatio-temporal interference settings, achieving near-optimal error rates.

Contribution

It proposes a novel clustered switchback design and a truncated Horvitz-Thompson estimator that handle non-stationarity, spatial, and temporal interference, with theoretical guarantees.

Findings

Achieves near-optimal mean squared error for sparse graphs.

Generalizes previous results on interference and experimentation.

Validated through simulation studies.

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 $\tilde O(1/NT)$ 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.