  Recent work on policy learning from observational data has highlighted the
importance of efficient policy evaluation and has proposed reductions to
weighted (cost-sensitive) classification. But, efficient policy evaluation need
not yield efficient estimation of policy parameters. We consider the estimation
problem given by a weighted surrogate-loss classification reduction of policy
learning with any score function, either direct, inverse-propensity weighted,
or doubly robust. We show that, under a correct specification assumption, the
weighted classification formulation need not be efficient for policy
parameters. We draw a contrast to actual (possibly weighted) binary
classification, where correct specification implies a parametric model, while
for policy learning it only implies a semiparametric model. In light of this,
we instead propose an estimation approach based on generalized method of
moments, which is efficient for the policy parameters. We propose a particular
method based on recent developments on solving moment problems using neural
networks and demonstrate the efficiency and regret benefits of this method
empirically.
