  We consider the problem of estimating and inferring treatment effects in
randomized experiments. In practice, stratified randomization, or more
generally, covariate-adaptive randomization, is routinely used in the design
stage to balance the treatment allocations with respect to a few variables that
are most relevant to the outcomes. Then, regression is performed in the
analysis stage to adjust the remaining imbalances to yield more efficient
treatment effect estimators. Building upon and unifying the recent results
obtained for ordinary least squares adjusted estimators under
covariate-adaptive randomization, this paper presents a general theory of
regression adjustment that allows for arbitrary model misspecification and the
presence of a large number of baseline covariates. We exemplify the theory on
two Lasso-adjusted treatment effect estimators, both of which are optimal in
their respective classes. In addition, nonparametric consistent variance
estimators are proposed to facilitate valid inferences, which work irrespective
of the specific randomization methods used. The robustness and improved
efficiency of the proposed estimators are demonstrated through a simulation
study and a clinical trial example. This study sheds light on improving
treatment effect estimation efficiency by implementing machine learning methods
in covariate-adaptive randomized experiments.
