arXiv:2505.08908math.STcs.LG2025-05被引 7

提出可识别反事实风险的决策理论,提升政策评估精度。

Statistical Decision Theory with Counterfactual Loss

  • 基于可加性反事实损失,实现个体层面决策质量评估
  • 在多处理选项下,推荐结果比传统方法更优
  • 适合需权衡决策难易与准确性的场景,如司法裁判

许多研究者将经典统计决策理论用于评估治疗选择和学习最优策略。然而,该框架仅依赖所选行动下的实际结果,忽略反事实信息,无法在个体层面评估决策相对于可行替代方案的质量,这在某些场景中至关重要。例如,在保释决定中,法官需权衡释放后的犯罪预防与对嫌疑人施加不必要负担的风险。核心挑战在于识别:因每单位仅观测一个潜在结果,反事实风险通常不可识别。我们证明,在强忽略性假设下,反事实风险可识别当且仅当损失函数在潜在结果上为可加性。进一步表明,当超过两种处理选项时,可加性反事实损失可产生与标准损失不同的治疗建议。可加性反事实损失不仅捕捉决策准确性,还反映决策难度,而标准损失仅反映准确性。最后,我们引入一种符号线性逆规划,无需数据即可判断给定反事实损失是否导致可识别风险。

原文摘要 · Abstract (English)

Many researchers apply classical statistical decision theory to evaluate treatment choices and learn optimal policies. However, because this framework relies solely on realized outcomes under chosen actions and ignores counterfactuals, it cannot assess the quality of a decision relative to feasible alternatives at the unit level, which is an important requirement in some settings. For example, in pretrial bail decisions, a judge must balance crime prevention upon release against the risk of imposing unnecessary burdens on arrestees. A central challenge in this framework is identification: since only one potential outcome is observed per unit, counterfactual risk is typically not identifiable. We show that, under strong ignorability, counterfactual risk is identifiable if and only if the loss is additive in the potential outcomes. We further demonstrate that additive counterfactual losses can yield treatment recommendations that differ from those based on standard losses when more than two treatment options are available. We show that additive counterfactual losses capture not only decision accuracy but also decision difficulty, whereas standard losses reflect accuracy alone. Finally, we introduce a symbolic linear inverse program that determines whether a given counterfactual loss yields an identifiable risk, without requiring data.

决策理论反事实分析因果推断可识别性

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