Balancing Covariates in Randomized Experiments with the Gram-Schmidt Walk Design

Understand

The design of experiments involves a compromise between covariate balance and robustness.

• This paper provides a formalization of this trade-off and describes an experimental design that allows experimenters to navigate it.
• The design is specified by a robustness parameter that bounds the worst-case mean squared error of an estimator of the average treatment effect.
• Subject to the experimenter's desired level of robustness, the design aims to simultaneously balance all linear functions of potentially many covariates.