Algorithmic predictions are increasingly used to inform the allocation of scarce resources. The promise of these methods is that, through machine learning, they can better identify the people who would benefit most from interventions. Recently, however, several works have called this assumption into question by demonstrating the existence of settings where simple, unit-level allocation strategies can meet or even exceed the performance of those based on individual-level targeting. Separately, other works have objected to individual-level targeting on privacy grounds, leading to an unusual situation where a single solution, unit-level targeting, is recommended for reasons of both privacy and utility. Motivated by the desire to fully understand the interplay of privacy and targeting levels, we initiate the study of aid allocation systems that satisfy differential privacy, synthesizing existing works on private optimization with the economic models of aid allocation used in the non-private literature. To this end, we investigate private variants of both individual and unit-level allocation strategies in both stochastic and distribution-free settings under a range of constraints on data availability. Through this analysis, we provide clean, interpretable bounds characterizing the tradeoffs between privacy, efficiency, and targeting precision in allocation.

翻译：算法预测正被越来越多地用于指导稀缺资源的分配。这些方法的承诺在于，通过机器学习，它们能更有效地识别最需要干预的人群。然而最近，一些研究通过证明存在某些场景——其中简单的群体级分配策略能够达到甚至超越基于个体级定位的策略——对这一假设提出了质疑。另一些研究则从隐私角度反对个体级定位，这导致了一种独特局面：出于隐私和效用的双重原因，群体级定位这一单一解决方案被推荐。受全面理解隐私与定位层次之间相互作用的愿望驱动，我们启动了对满足差分隐私的援助分配系统的研究，将现有关于私有优化的研究与非私有文献中使用的援助分配经济模型相结合。为此，我们探讨了个体和群体级分配策略在随机和非分布自由环境下的私有变体，并考虑了数据可用性的多种约束条件。通过这一分析，我们提供了清晰且可解释的界限，用以表征隐私、效率与分配精度之间的权衡关系。