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.

翻译：数据驱动的决策制定在医学和公共政策等高风险场景中扮演着重要角色。从观测数据中学习最优策略需要精心构建效用函数，使得其在总体中的期望值最大化。尽管研究者通常使用仅依赖观测结果的效用函数，但在许多场景中，决策者的效用函数更应通过所有行动下潜在结果的联合集合来刻画。例如，希波克拉底誓言中“首先不伤害”的原则意味着，导致本可无需治疗即可存活的病人死亡的代价，大于放弃挽救生命治疗的代价。我们考虑此类具有不对称反事实效用函数的最优策略学习，该函数关注潜在结果的联合集合。研究表明，不对称反事实效用会导致期望效用函数不可识别，因此我们首先对其进行部分识别。借鉴统计决策理论，我们通过最小化相对于不同备选策略的最大期望效用损失，导出极小化极大决策规则。进一步证明，通过求解中间分类问题可从观测数据中学得极小化极大损失决策规则，并建立该过程的有限样本超额期望效用损失受这些中间分类器遗憾值约束的结论。我们将这一概念框架和方法论应用于针对疑似肺动脉高压患者是否使用右心导管术的决策问题。