  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.
