We consider the problem of A-B testing when the impact of a treatment is marred by a large number of covariates. This is the situation in a number of modern applications of A-B testing (such as in adTech and e-commerce) as well as in more traditional applications (such as clinical trials). Randomization can be highly inefficient in such settings, and thus we consider the problem of optimally allocating test subjects to either treatment with a view to maximizing the efficiency of our estimate of the treatment effect. Our main contribution is a tractable algorithm that is near optimal under a broad set of assumptions. Specifically, we provide an algorithm for this problem in the online setting where subjects arrive, and must be assigned, sequentially. We also characterize the value of optimization and show that it can be expected to grow large with the number of covariates. Finally, using a real-world impression dataset, we show that our algorithms can be expected to yield substantial improvements to efficiency in practice. Joint work with Nikhil Bhat (AirBnB) and Ciamac Moallemi (Columbia)

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