The goal of uplift modeling is to recommend actions that optimize specific outcomes by determining which entities should receive treatment. One common approach involves two steps: first, an inference step that estimates conditional average treatment effects (CATEs), and second, an optimization step that ranks entities based on their CATE values and assigns treatment to the top k within a given budget. While uplift modeling typically focuses on binary treatments, many real-world applications are characterized by continuous-valued treatments, i.e., a treatment dose. This paper presents a predict-then-optimize framework to allow for continuous treatments in uplift modeling. First, in the inference step, conditional average dose responses (CADRs) are estimated from data using causal machine learning techniques. Second, in the optimization step, we frame the assignment task of continuous treatments as a dose-allocation problem and solve it using integer linear programming (ILP). This approach allows decision-makers to efficiently and effectively allocate treatment doses while balancing resource availability, with the possibility of adding extra constraints like fairness considerations or adapting the objective function to take into account instance-dependent costs and benefits to maximize utility. The experiments compare several CADR estimators and illustrate the trade-offs between policy value and fairness, as well as the impact of an adapted objective function. This showcases the framework's advantages and flexibility across diverse applications in healthcare, lending, and human resource management. All code is available on github.com/SimonDeVos/UMCT.

翻译：提升建模的目标是通过确定哪些实体应接受处理来推荐优化特定结果的行为。一种常见方法包含两个步骤：首先，在推断步骤中估计条件平均处理效应（CATEs）；其次，在优化步骤中根据实体的CATE值进行排序，并在给定预算内对前k个实体分配处理。虽然提升建模通常关注二元处理，但许多实际应用具有连续值处理（即处理剂量）的特征。本文提出一种先预测后优化的框架，以允许在提升建模中使用连续处理。首先，在推断步骤中，使用因果机器学习技术从数据中估计条件平均剂量响应（CADRs）。其次，在优化步骤中，我们将连续处理的分配任务构建为剂量分配问题，并使用整数线性规划（ILP）进行求解。该方法使决策者能够在平衡资源可用性的同时高效分配处理剂量，并可添加额外约束（如公平性考量）或调整目标函数以纳入实例相关的成本与收益，从而实现效用最大化。实验比较了多种CADR估计器，并阐述了策略价值与公平性之间的权衡，以及调整后目标函数的影响。这展示了该框架在医疗保健、信贷和人力资源管理等多种应用中的优势与灵活性。所有代码可在github.com/SimonDeVos/UMCT获取。