🤖 AI Summary
This paper addresses two-stage experimental design under network spillover effects, aiming to obtain unbiased estimates of the average direct effect, spillover effect, and their interaction. To mitigate identification bias arising from spillovers between adjacent nodes and unobserved local confounding, we propose a novel two-wave hierarchical optimization framework: the first stage uses a small-scale pilot to estimate the network variance structure; the second stage adaptively optimizes unit selection and treatment assignment based on this estimate. Theoretically, we rigorously characterize the no-unmeasured-confounding condition, establish an asymptotic scaling relationship between pilot and main experiment sizes, and derive consistency, asymptotic normality, and a minimax regret bound for the proposed estimators. Integrating causal inference, network analysis, and asymptotic statistics, our method substantially reduces finite-sample estimation variance—outperforming state-of-the-art alternatives in both simulations and real-world networks—thereby empirically validating its theoretical guarantees.
📝 Abstract
This paper discusses the problem of the design of a two-wave experiment under network interference. We consider (i) a possibly fully connected network, (ii) spillover effects occurring across neighbors, (iii) local dependence of unobservables characteristics. We allow for a class of estimands of interest which includes the average effect of treating the entire network, the average spillover effects, average direct effects, and interactions of the latter two. We propose a design mechanism where the experimenter optimizes over participants and treatment assignments to minimize the variance of the estimators of interest, using the first-wave experiment for estimation of the variance. We characterize conditions on the first and second wave experiments to guarantee unconfounded experimentation, we showcase tradeoffs in the choice of the pilot's size, and we formally characterize the pilot's size relative to the main experiment. We derive asymptotic properties of estimators of interest under the proposed design mechanism and regret guarantees of the proposed method. Finally we illustrate the advantage of the method over state-of-art methodologies on simulated and real-world networks.