Current subgroup identification methods typically follow a two-step approach: first estimate conditional average treatment effects and then apply thresholding or rule-based procedures to define subgroups. While intuitive, this decoupled approach fails to incorporate key constraints essential for real-world clinical decision-making, such as subgroup size and propensity overlap. These constraints operate on fundamentally different axes than CATE estimation and are not naturally accommodated within existing frameworks, thereby limiting the practical applicability of these methods. We propose a unified optimization framework that directly solves the primal constrained optimization problem to identify optimal subgroups. Our key innovation is a reformulation of the constrained primal problem as an unconstrained differentiable min-max objective, solved via a gradient descent-ascent algorithm. We theoretically establish that our solution converges to a feasible and locally optimal solution. Unlike threshold-based CATE methods that apply constraints as post-hoc filters, our approach enforces them directly during optimization. The framework is model-agnostic, compatible with a wide range of CATE estimators, and extensible to additional constraints like cost limits or fairness criteria. Extensive experiments on synthetic and real-world datasets demonstrate its effectiveness in identifying high-benefit subgroups while maintaining better satisfaction of constraints.

翻译：现有子群识别方法通常遵循两步法：首先估计条件平均处理效应，再通过阈值或规则化程序定义子群。这种解耦方法虽直观，却未能纳入实际临床决策所需的关键约束条件（如子群规模与倾向性重叠）。这些约束在本质上与CATE估计处于不同维度，难以在现有框架内自然兼容，从而限制了此类方法的实际应用性。本文提出一种统一优化框架，通过直接求解原始约束优化问题来识别最优子群。我们的核心创新在于将约束原始问题重构为无约束可微极小-极大目标，并通过梯度下降-上升算法求解。我们从理论上证明该解可收敛至可行且局部最优的解。不同于将约束作为后处理过滤器应用的基于阈值的CATE方法，我们的方法在优化过程中直接施加约束。该框架具有模型无关性，可兼容多种CATE估计器，并能扩展至成本限制或公平性准则等额外约束。在合成和真实数据集上的大量实验表明，该方法在保持更好约束满足度的同时，能有效识别高效益子群。