Experimental designs that balance pre-treatment measurements (baseline covariates) are in pervasive use throughout the practice of controlled experimentation, including randomized block designs, pairwise-matched designs, and re-randomization. We argue that no balance better than complete randomization can be achieved without partial structural knowledge about the treatment effects and therefore such knowledge must be present in these experiments. We propose a novel framework for formulating such knowledge that recovers these designs as optimal under certain modeling choices and suggests new optimal designs that are based on nonparametric modeling and offer significant gains in precision and power. We characterize the unbiasedness, variance, and consistency of resulting estimators; solve the design problem; and develop appropriate inferential algorithms. We make connections to Bayesian experimental design and extensions to dealing with non-compliance.
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