Partial Identification Learning with Categorical Treatments for Individualized Treatment Rules
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AI 根据所提供的论文材料归类：摘要以因果界、工具变量和未观测混杂下的个体化处理决策为核心。
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分类处理下个体化处理规则的部分识别学习
- 研究问题
- 当未观测混杂使处理效应只能部分识别时，如何在多个离散处理选项中学习个体化规则，并限制最坏情形决策损失？
- 方法与思路
- 作者利用因果界构造广义极小极大损失，将处理映射至正则单纯形顶点，再以可微加权替代风险学习决策规则。
- 材料陈述的贡献
- 摘要称，该框架扩展至分类处理、结果和工具变量，建立替代风险与原问题的联系，并给出有限样本预言机不等式。
- 阅读关注点
- 核对各因果结构下界的构造、替代风险与原决策目标的对应条件，以及核实现满足收敛条件的具体要求。
- 阅读边界
- 所据为 arXiv 预印本，同行评审或期刊接收未经核实；部分识别仍需因果假设，摘要未列全，也未报告比较数值。
原文摘要
We develop a partial identification learning framework for individualized treatment rules (ITRs) with categorical treatments, outcomes, and instrumental variables. Rather than relying on strong causal assumptions required for point identification, our framework leverages causal bounds to characterize the optimal treatment decision. Existing methods for ITR optimization under partial identification are largely restricted to binary treatment settings and the bounds derived by Balke and Pearl under the canonical instrumental variable design. We extend this framework to accommodate a broader class of causal structures as well as scenarios with categorical treatment, outcome, and instrumental variables. We introduce a generalized minimax loss criterion for treatment selection from among more than two options, which minimizes the maximum possible difference between the chosen and the optimal treatment based on partial identification bounds. To construct the ITR, we use a symmetric embedding strategy that maps discrete treatments to the vertices of a regular simplex, avoiding the geometric inconsistencies of standard one-vs-rest approaches. We derive a differentiable, weighted surrogate risk function and show that optimizing it solves the original problem. Furthermore, we provide finite sample convergence rates via an oracle inequality under general regularity conditions, which we show are satisfied by a kernel based implementation. Numerical experiments demonstrate that the framework yields ITRs significantly closer to the oracle ITR compared to existing alternatives in settings with unmeasured confounding.