  Randomized trials, also known as A/B tests, are used to select between two
policies: a control and a treatment. Given a corresponding set of features, we
can ideally learn an optimized policy P that maps the A/B test data features to
action space and optimizes reward. However, although A/B testing provides an
unbiased estimator for the value of deploying B (i.e., switching from policy A
to B), direct application of those samples to learn the the optimized policy P
generally does not provide an unbiased estimator of the value of P as the
samples were observed when constructing P. In situations where the cost and
risks associated of deploying a policy are high, such an unbiased estimator is
highly desirable.
  We present a procedure for learning optimized policies and getting unbiased
estimates for the value of deploying them. We wrap any policy learning
procedure with a bagging process and obtain out-of-bag policy inclusion
decisions for each sample. We then prove that inverse-propensity-weighting
effect estimator is unbiased when applied to the optimized subset. Likewise, we
apply the same idea to obtain out-of-bag unbiased per-sample value estimate of
the measurement that is independent of the randomized treatment, and use these
estimates to build an unbiased doubly-robust effect estimator. Lastly, we
empirically shown that even when the average treatment effect is negative we
can find a positive optimized policy.
