Towards Optimal Variance Reduction in Online Controlled Experiments

Abstract: We study optimal variance reduction solutions for count and ratio metrics in online controlled experiments. Our methods leverage flexible machine learning tools to incorporate covariates that are independent from the treatment but have predictive power for the outcomes, and employ the cross-fitting technique to remove the bias in complex machine learning models. We establish CLT-type asymptotic inference based on our estimators under mild convergence conditions. Our procedures are optimal (efficient) for the corresponding targets as long as the machine learning estimators are consistent, without any requirement for their convergence rates. In complement to the general optimal procedure, we also derive a linear adjustment method for ratio metrics as a special case that is computationally efficient and can flexibly incorporate any pre-treatment covariates. We evaluate the proposed variance reduction procedures with comprehensive simulation studies and provide practical suggestions regarding commonly adopted assumptions in computing ratio metrics. When tested on real online experiment data from LinkedIn, the proposed optimal procedure for ratio metrics can reduce up to 80\% of variance compared to the standard difference-in-mean estimator and also further reduce up to 30\% of variance compared to the CUPED approach by going beyond linearity and incorporating a large number of extra covariates.