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We study regression adjustment with general function class approximations forestimating the average treatment effect in the design-based setting. Standardregression adjustment involves bias due to sample re-use, and this bias leadsto behavior that is sub-optimal in the sample size, and/or imposes restrictiveassumptions. Our main contribution is to introduce a novel decorrelation-basedapproach that circumvents these issues. We prove guarantees, both asymptoticand non-asymptotic, relative to the oracle functions that are targeted by agiven regression adjustment procedure. We illustrate our method by applying itto various high-dimensional and non-parametric problems, exhibiting improvedsample complexity and weakened assumptions relative to known approaches.

A decorrelation method for general regression adjustment in randomized experiments