A fundamental question in data-driven decision making is how to quantify the uncertainty of predictions in ways that can usefully inform downstream action. This interface between prediction uncertainty and decision-making is especially important in risk-sensitive domains, such as medicine. In this paper, we develop decision-theoretic foundations that connect uncertainty quantification using prediction sets with risk-averse decision-making. Specifically, we answer three fundamental questions: (1) What is the correct notion of uncertainty quantification for risk-averse decision makers? We prove that prediction sets are optimal for decision makers who wish to optimize their value at risk. (2) What is the optimal policy that a risk averse decision maker should use to map prediction sets to actions? We show that a simple max-min decision policy is optimal for risk-averse decision makers. Finally, (3) How can we derive prediction sets that are optimal for such decision makers? We provide an exact characterization in the population regime and a distribution free finite-sample construction. Answering these questions naturally leads to an algorithm, Risk-Averse Calibration (RAC), which follows a provably optimal design for deriving action policies from predictions. RAC is designed to be both practical-capable of leveraging the quality of predictions in a black-box manner to enhance downstream utility-and safe-adhering to a user-defined risk threshold and optimizing the corresponding risk quantile of the user's downstream utility. Finally, we experimentally demonstrate the significant advantages of RAC in applications such as medical diagnosis and recommendation systems. Specifically, we show that RAC achieves a substantially improved trade-off between safety and utility, offering higher utility compared to existing methods while maintaining the safety guarantee.

本研究解决了如何在风险敏感领域（如医学）中量化预测不确定性的问题，提出了一种通过预测集连接不确定性量化与风险规避决策的方法。关键发现是，风险规避决策者的最佳策略是采用简单的最大-最小决策政策，研究成果在医疗诊断与推荐系统中显示了显著的安全性与效用之间的优势折衷。

符合预测的决策理论基础：风险规避代理的最佳不确定性量化