为反事实决策设计带覆盖保证的预测集,提升高风险决策可靠性。
Prediction Sets for Counterfactual Decisions: Coverage, Optimality, and Conformal Prediction

- 提出政策耦合覆盖率,让预测集与行动规则协同优化。
- 在真实邮件营销实验中,新方法比现有方法提升更多收益且覆盖有效。
- 适合需要兼顾准确性和决策鲁棒性的医疗、金融等场景。
预测被广泛用于高风险决策,如治疗选择和政策制定。为应对不完美预测带来的不确定性,基于置信推断的方法(如共形预测)可构建具有覆盖保证的预测集。然而,统计有效性并不能直接决定最优决策。这一差距在反事实情境下尤为显著——实际结果取决于所采取的行动,因此不确定性无法独立于决策规则定义。本文建立了一个决策理论框架,用于不确定信息驱动的反事实决策。提出新的‘政策耦合覆盖率’概念:即预测集自身诱导行动后,实际结果的覆盖概率。该概念具三重作用:第一,支撑一种自然的最大最小规则,在分布模糊性下实现极小极大最优;第二,以政策耦合覆盖为目标优化预测集,等价于更强的普遍覆盖形式及直接的风险规避策略与效用证书优化,从而给出总体最优预测集的显式形式;第三,提出两阶段算法PC-RACP,可近似求得这些最优集,并保持严格的有限样本覆盖。模拟与真实邮件营销实验表明,PC-RACP在保持覆盖有效性的同时,实现了更高效用;忽略反事实结构会导致有效性与效用双重损失。
原文摘要 · Abstract (English)
Predictions are increasingly used to guide high-stakes decisions, from treatment selection to policy making. To ensure reliability with imperfect predictions, uncertainty quantification methods such as conformal prediction build prediction sets with coverage guarantees. However, statistical validity alone does not immediately determine the decisions to take, nor the optimality thereof. This gap is especially delicate in counterfactual settings where the outcome that materializes depends on the action taken, so uncertainty cannot be specified independently of the decision rule. We develop a decision-theoretic framework for uncertainty-informed counterfactual decisions. We identify a novel notion of \emph{policy-coupled coverage} -- namely, coverage of the realized outcome under the action induced by the prediction sets themselves -- as the optimal and lossless interface between uncertainty and action. It plays three roles. First, it justifies acting via a natural max-min rule as minimax-optimal under distributional ambiguity. Second, optimizing prediction sets under policy-coupled coverage is equivalent both to a stronger universal-coverage formulation and to the direct risk-averse optimization over policies and utility certificates; this equivalence yields the explicit form of the population-optimal prediction sets. Third, it admits a two-stage procedure, Policy-Coupled Risk-Averse Conformal Prediction (PC-RACP), that approximates these optimal sets with rigorous finite-sample coverage. Simulations and a real email-marketing experiment confirm that PC-RACP delivers higher utility than existing approaches while maintaining valid coverage, and that ignoring the counterfactual structure of the decision problem is suboptimal for both validity and utility.
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