Cluster Randomized Designs for One-Sided Bipartite Experiments

The conclusions of randomized controlled trials may be biased when the outcome of one unit depends on the treatment status of other units, a problem known as \textit{interference}. In this work, we study interference in the setting of one-sided bipartite experiments in which the experimental units---where treatments are randomized and outcomes are measured---do not interact directly. Instead, their interactions are mediated through their connections to \textit{interference units} on the other side of the graph. Examples of this type of interference are common in marketplaces and two-sided platforms. The \textit{cluster-randomized design} is a popular method to mitigate interference when the graph is known, but it has not been well-studied in the one-sided bipartite experiment setting. In this work, we formalize a natural model for interference in one-sided bipartite experiments using the exposure mapping framework. We first exhibit settings under which existing cluster-randomized designs fail to properly mitigate interference under this model. We then show that minimizing the bias of the difference-in-means estimator under our model results in a balanced partitioning clustering objective with a natural interpretation. We further prove that our design is minimax optimal over the class of linear potential outcomes models with bounded interference. We conclude by providing theoretical and experimental evidence of the robustness of our design to a variety of interference graphs and potential outcomes models.