  Choosing optimal (or at least better) policies is an important problem in
domains from medicine to education to finance and many others. One approach to
this problem is through controlled experiments/trials - but controlled
experiments are expensive. Hence it is important to choose the best policies on
the basis of observational data. This presents two difficult challenges: (i)
missing counterfactuals, and (ii) selection bias. This paper presents
theoretical bounds on estimation errors of counterfactuals from observational
data by making connections to domain adaptation theory. It also presents a
principled way of choosing optimal policies using domain adversarial neural
networks. We illustrate the effectiveness of domain adversarial training
together with various features of our algorithm on a semi-synthetic breast
cancer dataset and a supervised UCI dataset (Statlog).
