  We study the problem of treatment effect estimation in randomized experiments
with high-dimensional covariate information, and show that essentially any
risk-consistent regression adjustment can be used to obtain efficient estimates
of the average treatment effect. Our results considerably extend the range of
settings where high-dimensional regression adjustments are guaranteed to
provide valid inference about the population average treatment effect. We then
propose cross-estimation, a simple method for obtaining finite-sample-unbiased
treatment effect estimates that leverages high-dimensional regression
adjustments. Our method can be used when the regression model is estimated
using the lasso, the elastic net, subset selection, etc. Finally, we extend our
analysis to allow for adaptive specification search via cross-validation, and
flexible non-parametric regression adjustments with machine learning methods
such as random forests or neural networks.
