Supplementary Material for Machine Learning for Variance Reduction in Online Experiments

In this supplementary material, we provide the proof of all theoretical results stated in the paper. We complete the proof in 8 steps by showing statements 1 - 8 above. Markov's inequality the first term on the RHS is also O This follows from Step 8 and the fact that by Chebyshev's inequality, The reasoning here is similar to Step 1. Since the number of splits K is bounded, we only need to verify for any k { 1, 2,...,K }, null null null null 1 n null Below we'll prove 1 n null Combining the above, we obtain (30). In the last inequality we utilize (32).