  Data-driven decision making plays an important role even in high stakes
settings like medicine and public policy. Learning optimal policies from
observed data requires a careful formulation of the utility function whose
expected value is maximized across a population. Although researchers typically
use utilities that depend on observed outcomes alone, in many settings the
decision maker's utility function is more properly characterized by the joint
set of potential outcomes under all actions. For example, the Hippocratic
principle to "do no harm" implies that the cost of causing death to a patient
who would otherwise survive without treatment is greater than the cost of
forgoing life-saving treatment. We consider optimal policy learning with
asymmetric counterfactual utility functions of this form that consider the
joint set of potential outcomes. We show that asymmetric counterfactual
utilities lead to an unidentifiable expected utility function, and so we first
partially identify it. Drawing on statistical decision theory, we then derive
minimax decision rules by minimizing the maximum expected utility loss relative
to different alternative policies. We show that one can learn minimax loss
decision rules from observed data by solving intermediate classification
problems, and establish that the finite sample excess expected utility loss of
this procedure is bounded by the regret of these intermediate classifiers. We
apply this conceptual framework and methodology to the decision about whether
or not to use right heart catheterization for patients with possible pulmonary
hypertension.
