Policy design in experiments with unknown interference

This paper studies experimental designs for estimation and inference on welfare-maximizing policies in the presence of spillover effects. Units are organized into a finite number of large clusters and interact in unknown ways within each cluster. As a first contribution, I introduce a single-wave experiment that, by carefully varying the randomization across cluster pairs, estimates the marginal effect of a change in treatment probabilities, taking spillover effects into account. Using the marginal effect, I propose a test for policy optimality. As a second contribution, I design a multiple-wave experiment to estimate treatment rules and maximize welfare. I derive strong small-sample guarantees on the difference between the maximum attainable welfare and the welfare evaluated at the estimated policy. I illustrate the method's properties in simulations calibrated to existing experiments on information diffusion and cash-transfer programs, and in a large scale field experiment implemented in rural Pakistan.