This paper discusses the problem of the design of experiments under network interference. We allow for a possibly fully connected network and a general class of estimands , which encompasses average treatment and average spillover effects, as well as estimands obtained from interactions of the  two. We discuss a near-optimal design mechanism , where the experimenter optimizes over participants and treatment assignments to minimize the variance of the estimators of interest, using a first-wave experiment for estimation of the variance. We guarantee valid asymptotic inference on causal effects using either parametric or non-parametric estimators under the proposed experimental design, allowing for local dependence of potential outcomes, arbitrary dependence of the treatment assignment indicators, and spillovers across units. We showcase asymptotic optimality and finite-sample upper bounds on the regret of the  proposed design mechanism . Simulations illustrate the advantage of the method over state-of-art methodologies  .
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 .
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