Conditional Average Treatment Effect Distillation for Hypothetical State-Intervention Targeting Under Budget Constraints

arXiv:2610.25627v1 Announce Type: new Abstract: Personalized public-health targeting must capture heterogeneous intervention benefits while remaining interpretable under resource constraints. Flexible causal-effect models can be hard to operationalize, while coarse subgroup policies may lose individualized effect information. We study budget-constrained hypothetical state interventions in observational data without a logged historical decision policy. For obesity, elevated glucose, and lifetime smoking-history states, causal-structure-informed pretreatment covariates are prespecified, with capacity capped at 70% of those observed in the adverse state. We evaluate causal distillation where Causal Forest and Bayesian Causal Forest teachers estimate conditional average treatment effects (CATEs), which decision tree and random forest students approximate. We compare individualized policies with unsupervised K-means subgroup policies and supervised causal-tree policies with leaf counts matched to K-means cluster counts. Observational policies are assessed on held-out data using a doubly robust estimator, bootstrap uncertainty, and decision-focused teacher-student fidelity measures. Across PIMA obesity and glucose and NHANES smoking-history experiments, each distilled student was within 0.011 absolute utility of its teacher, with allocation Jaccard similarities of 0.738-0.937. K-means and causal-tree policies were also competitive, with the highest point-estimate policy varying by application. Prespecified paired comparisons were nonsignificant after Holm adjustment, while near-budget-boundary agreement was less stable than global fidelity for some teacher-student pairs. Findings support causal distillation for translating flexible effect models into simpler budgeted targeting rules, although observational estimates depend on causal-identification assumptions and require longitudinal or prospective validation.