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：算法预测日益被用于指导稀缺资源的分配。这些方法的前景在于，通过机器学习，它们能更好地识别哪些人能从干预措施中获益最多。然而，近期多项研究对这一假设提出质疑，指出存在一些情境，其中简单的单位级分配策略能达到甚至超越基于个体级定位的策略的性能。与此同时，其他研究出于隐私考量反对个体级定位，导致一种特殊局面：基于隐私和效用两方面的原因，单位级定位这一单一解决方案均受到推荐。出于全面理解隐私与定位层级之间相互作用的动机，我们启动了满足差分隐私的援助分配系统研究，将现有关于隐私优化的研究成果与非隐私文献中使用的援助分配经济模型相结合。为此，我们研究了在数据可用性受多种约束的情况下，随机环境与无分布环境中个体级与单位级分配策略的隐私变体。通过这一分析，我们提供了清晰、可解释的界限，用以描述分配过程中隐私、效率与定位精度之间的权衡关系。