Policy choice in experiments with unknown interference

This paper discusses experimental design for inference and estimation of individualized treatment allocation rules in the presence of unknown interference. We consider a setting where units are organized into large, finitely many independent clusters and interact over unobserved dimensions within each cluster. The contribution of this paper is two-fold. First, we design a short pilot study with few clusters to test whether there exists a welfare-improving treatment configuration and hence worth learning by conducting a larger scale experiment. We propose a practical test that uses information on the marginal effect of the policy on welfare to compare the base-line intervention against any possible alternative. Second, we introduce a sequential randomization procedure to estimate welfare-maximizing individual treatment allocation rules valid under unobserved (and partial) interference. We propose non-parametric estimators of direct treatments and marginal spillover effects, which serve for hypothesis testing and policy-design. We derive the estimators' asymptotic properties, and small sample regret guarantees of the policy estimated through the sequential experiment. Finally, we illustrate the method's advantage in simulations calibrated to an existing experiment on information diffusion.