Recent methodological research in causal inference has focused on effects of stochastic interventions, which assign treatment randomly, often according to subject-specific covariates. In this work, we demonstrate that the usual notion of stochastic interventions have a surprising property: when there is unmeasured confounding, bounds on their effects do not collapse when the policy approaches the observational regime. As an alternative, we propose to study generalized policies, treatment rules that can depend on covariates, the natural value of treatment, and auxiliary randomness. We show that certain generalized policy formulations can resolve the "non-collapsing" bound issue: bounds narrow to a point when the target treatment distribution approaches that in the observed data. Moreover, drawing connections to the theory of optimal transport, we characterize generalized policies that minimize worst-case bound width in various sensitivity analysis models, as well as corresponding sharp bounds on their causal effects. These optimal policies are new, and can have a more parsimonious interpretation compared to their usual stochastic policy analogues. Finally, we develop flexible, efficient, and robust estimators for the sharp nonparametric bounds that emerge from the framework.

翻译：近期因果推断的方法学研究聚焦于随机干预效应，这类干预通常依据受试者特定协变量进行随机化处理。本文揭示了传统随机干预概念的一个反直觉特性：当存在未测量混杂时，其效应边界在干预策略趋近观测机制时不会收敛。为此，我们提出研究广义策略——这种处理规则可同时依赖于协变量、处理的自然值及辅助随机变量。我们证明特定广义策略的数学表述能够解决"非收敛边界"问题：当目标处理分布趋近观测数据分布时，效应边界会收缩至单点。通过建立与最优传输理论的联系，我们刻画了在多种敏感性分析模型中能最小化最坏情况边界宽度的广义策略，并给出相应因果效应的尖锐边界。这些最优策略具有创新性，且相较于传统随机策略往往具备更简约的解释力。最后，我们为该框架衍生的尖锐非参数边界开发了灵活、高效且稳健的估计方法。