不确定决策系统中的共形化安全可行集

中文摘要 AI 辅助

安全关键决策系统通常需要下游优化器从未观测标签$Y$决定的未知可行集中进行选择。给定上下文$X$，目标是构造一个包含在预言可行集$A(X,Y)$中的安全子集$D(X)$，其概率至少为$1-\alpha$。现有的共形方法通常构造未观测标签$Y$的预测集，并保留对该集合中每个值都安全的决策。尽管有效，但这需要一个比集合包含更强的事件作为中间条件。我们提出定向包含安全校准（DISC），一种共形框架，通过将包含事件的验证简化为一个标量临界包含分数来直接控制该事件发生的概率。给定一个预训练的候选可行集嵌套族，DISC为每个带标签的观测分配最小的嵌套层级，在该层级上对应的子集包含于$A(X,Y)$中，并在测试时使用经验分位数构造安全可行集。在数据可交换性条件下，这产生了有限样本、无分布假设的包含保证。在两种实用的集合族下，我们证明DISC产生的安全可行集包含相应校准基线所获得的集合。我们进一步开发了基于优化的分数计算和用于学习子集族的决策感知程序。在连续和结构化决策问题上的实验表明，DISC在实现目标包含保证的同时产生了更大的可行区域。

英文摘要

Safety-critical decision systems often require a downstream optimizer to choose from an unknown feasible set determined by an unobserved label $Y$. Given a context $X$, the goal is to construct a safe subset $D(X)$ contained in the oracle feasible set $A(X,Y)$ with probability at least $1-α$. Existing conformal approaches typically construct a prediction set of the unobserved label $Y$ and retain decisions that are safe for every value in this set. Although valid, this requires a stronger intermediate event than set inclusion. We propose Directed Inclusion Safety Calibration (DISC), a conformal framework that directly controls the probability of this inclusion event by reducing its verification to a scalar critical-inclusion score. Given a pretrained nested family of candidate feasible sets, DISC assigns each labeled observation the smallest nestedness level at which the corresponding subset is contained in $A(X,Y)$, and constructs the safe feasible set using an empirical quantile at test-time. With data exchangeability, this yields a finite-sample, distribution-free inclusion guarantee. Under two practical set families, we show that DISC produces a safe feasible set containing that obtained by the corresponding calibration baseline. We further develop optimization-based score computation and decision-aware procedures for learning subset families. Experiments across continuous and structured decision problems show that DISC achieves the target inclusion guarantee while producing larger feasible regions.

发表机构

• School of Management, Fudan University（复旦大学管理学院）
• School of Statistics and Data Science, Nankai University（南开大学统计与数据科学学院）
• School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学系）

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