  Counterfactual learning from observational data involves learning a
classifier on an entire population based on data that is observed conditioned
on a selection policy. This work considers this problem in an active setting,
where the learner additionally has access to unlabeled examples and can choose
to get a subset of these labeled by an oracle.
  Prior work on this problem uses disagreement-based active learning, along
with an importance weighted loss estimator to account for counterfactuals,
which leads to a high label complexity. We show how to instead incorporate a
more efficient counterfactual risk minimizer into the active learning
algorithm. This requires us to modify both the counterfactual risk to make it
amenable to active learning, as well as the active learning process to make it
amenable to the risk. We provably demonstrate that the result of this is an
algorithm which is statistically consistent as well as more label-efficient
than prior work.
