  In many areas, practitioners seek to use observational data to learn a
treatment assignment policy that satisfies application-specific constraints,
such as budget, fairness, simplicity, or other functional form constraints. For
example, policies may be restricted to take the form of decision trees based on
a limited set of easily observable individual characteristics. We propose a new
approach to this problem motivated by the theory of semiparametrically
efficient estimation. Our method can be used to optimize either binary
treatments or infinitesimal nudges to continuous treatments, and can leverage
observational data where causal effects are identified using a variety of
strategies, including selection on observables and instrumental variables.
Given a doubly robust estimator of the causal effect of assigning everyone to
treatment, we develop an algorithm for choosing whom to treat, and establish
strong guarantees for the asymptotic utilitarian regret of the resulting
policy.
