Will Our Treatment Policy Really Work? Multiscale Segmentation of Treatment-Benefit Regions

Heterogeneous treatment effect estimation informs a decision maker who benefits most, but not whether the resulting rule is deployable: how many distinct beneficiary groups must be handled, and what is lost when the segment budget is smaller. Existing policy learning methods impose constraints on capacity or the policy class, yet policies with identical value and coverage can have very different geometry and implementation cost. We study deployability through the topology of treatment-benefit superlevel sets. Connected components count distinct beneficiary segments, while persistence across nearby thresholds identifies segments stable to perturbations in the effect estimate and threshold. We propose a post-estimation deployability layer, compatible with any CATE estimator, that reports persistent zeroth Betti numbers before and after overlap trimming and, when more segments survive than the budget allows, returns a conservative policy targeting those with the largest estimated gains. We prove that persistent segmentation lower-bounds conservative policy complexity, insufficient segment capacity forces regret, and uniform accuracy of the effect estimate transfers to stable segmentation summaries. Empirical studies show that the proposed method uncovers deployment failure modes not captured by existing policy learning approaches.