Efficiently allocating treatments with a budget constraint constitutes an important challenge across various domains. In marketing, for example, the use of promotions to target potential customers and boost conversions is limited by the available budget. While much research focuses on estimating causal effects, there is relatively limited work on learning to allocate treatments while considering the operational context. Existing methods for uplift modeling or causal inference primarily estimate treatment effects, without considering how this relates to a profit maximizing allocation policy that respects budget constraints. The potential downside of using these methods is that the resulting predictive model is not aligned with the operational context. Therefore, prediction errors are propagated to the optimization of the budget allocation problem, subsequently leading to a suboptimal allocation policy. We propose an alternative approach based on learning to rank. Our proposed methodology directly learns an allocation policy by prioritizing instances in terms of their incremental profit. We propose an efficient sampling procedure for the optimization of the ranking model to scale our methodology to large-scale data sets. Theoretically, we show how learning to rank can maximize the area under a policy's incremental profit curve. Empirically, we validate our methodology and show its effectiveness in practice through a series of experiments on both synthetic and real-world data.

翻译：在预算约束下高效分配资源是各领域面临的重大挑战。例如在市场营销中，利用促销活动定位潜在客户并提升转化率的行为受制于可用预算。当前研究虽多聚焦于因果效应估计，但针对考虑运营情境的分配策略学习研究相对有限。现有的增量建模或因果推断方法主要致力于估计处理效应，却未探讨其与遵循预算约束的利润最大化分配策略之间的关联。采用这些方法的潜在缺陷在于，其预测模型与运营情境存在偏差，导致预测误差会传导至预算分配优化问题，进而产生次优的分配策略。我们提出基于排序学习的替代方案：该方法通过按增量利润对实例进行优先级排序，直接学习分配策略。针对排序模型优化，我们设计了高效采样流程，使方法可扩展至大规模数据集。理论层面，我们论证了排序学习如何最大化策略增量利润曲线下的面积。实证层面，通过合成数据与真实数据的系列实验，我们验证了方法的有效性及其在实践中的表现。