This paper studies how to design two-wave experiments in the presence of spillovers for precise inference on treatment effects. We consider units connected through a single network, local dependence among individuals, and a general class of estimands encompassing average treatment and average spillover effects. We introduce a statistical framework for designing two-wave experiments with networks, where the researcher optimizes over participants and treatment assignments to minimize the variance of the estimators of interest, using a first-wave (pilot) experiment to estimate the variance. We derive guarantees for inference on treatment effects and regret guarantees on the variance obtained from the proposed design mechanism. Our results illustrate the existence of a trade-off in the choice of the pilot study and formally characterize the pilot's size relative to the main experiment. Simulations using simulated and real-world networks illustrate the advantages of the method.

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