提出新方法，让预测集在关键决策中更可靠，减少重大错误。
Optimal Decision-Making Based on Prediction Sets
- 基于最坏情况风险最小化设计决策策略，兼顾集内集外损失。
- 实验显示在医疗诊断等场景下，显著降低高代价错误率。
- 适合对安全要求高的场景，如医疗、自动驾驶等决策任务。
预测集可为任意机器学习模型提供保证：以指定概率覆盖未知测试结果。然而，如何利用这些预测集进行下游决策仍不明确。本文提出一种决策理论框架，旨在最小化与预测集覆盖率保证一致的最坏情况分布下的期望损失（风险）。首先刻画了固定预测集下的极小极大最优策略，表明其需权衡集合内部的最坏情况损失与集合外部潜在损失的惩罚。在此基础上，推导出在覆盖率约束下最小化鲁棒风险的最优预测集构造方法。最后，提出风险最优共形预测（ROCP）算法，可在保持有限样本无分布假设边际覆盖率的同时，直接优化风险最小化的预测集。在医学诊断和高安全性决策任务上的实证评估表明，相较于基线方法，ROCP显著减少了关键错误，尤其在集合外错误代价高昂时效果更优。
原文摘要 · Abstract (English)
Prediction sets can wrap around any ML model to cover unknown test outcomes with a guaranteed probability. Yet, it remains unclear how to use them optimally for downstream decision-making. Here, we propose a decision-theoretic framework that seeks to minimize the expected loss (risk) against a worst-case distribution consistent with the prediction set's coverage guarantee. We first characterize the minimax optimal policy for a fixed prediction set, showing that it balances the worst-case loss inside the set with a penalty for potential losses outside the set. Building on this, we derive the optimal prediction set construction that minimizes the resulting robust risk subject to a coverage constraint. Finally, we introduce Risk-Optimal Conformal Prediction (ROCP), a practical algorithm that targets these risk-minimizing sets while maintaining finite-sample distribution-free marginal coverage. Empirical evaluations on medical diagnosis and safety-critical decision-making tasks demonstrate that ROCP reduces critical mistakes compared to baselines, particularly when out-of-set errors are costly.
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