Unbiased variance reduction in randomized experiments

Abstract

This paper develops a flexible method for decreasing the variance of estimators for complex experiment effect metrics (e.g. ratio metrics) while retaining asymptotic unbiasedness. This method uses the auxiliary information about the experiment units to decrease the variance. The method can incorporate almost any arbitrary predictive model (e.g. linear regression, regularization, neural networks) to adjust the estimators. The adjustment involves some free parameters which can be optimized to achieve the smallest variance reduction given the predictive model performance. Also we approximate the achievable reduction in variance in fairly general settings mathematically. Finally, we use simulations to show the method works.