差分隐私多色差异与不可分割商品的公平分配
Differentially Private Multicolor Discrepancy and Fair Division of Indivisible Goods
- RIKEN Center for Advanced Intelligence Project（RIKEN先进智能项目中心）
- The University of Tokyo（东京大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在纯差分隐私下研究不可分割商品公平分配，提出条目私有算法实现共识无嫉妒性，显著改进依赖并给出下界。
AI中文摘要：
我们在纯差分隐私下研究不可分割商品的公平分配问题，延续了Manurangsi和Suksompong开创的研究方向。对于n个代理对m个商品具有非负可加效用且隐私参数固定的情况，我们给出一个条目私有算法，该算法以高概率实现共识无嫉妒性，最多移除O(√n+log³m)个商品。这大幅改善了先前普通无嫉妒性O(n log m)保证中对n的依赖，同时提供了更强的共识保证。一个关键成分是用于多色差异的私有算法，该算法可能具有独立的研究价值。我们的算法可能需要指数时间。在额外结构下，我们还获得了显著更强的保证：当所有物品价值属于大小为D的公共字母表时，我们给出一个多项式时间的条目私有算法，以高概率实现普通无嫉妒性，最多移除O(polylog(mD))个商品。最后，我们证明了一个Ω(log n)的下界，即在条目隐私下，对于足够多的商品，即使使用二元效用，也必须移除该数量的商品才能实现普通无嫉妒性。
英文摘要：
We study the fair division of indivisible goods under pure differential privacy, continuing the line of work initiated by Manurangsi and Suksompong. For $n$ agents with nonnegative additive utilities over $m$ goods and a fixed privacy parameter, we give an entry-private algorithm that, with high probability, achieves consensus envy-freeness up to $O(\sqrt n+\log^3 m)$ goods. This substantially improves the dependence on $n$ over the previous $O(n\log m)$ guarantee for ordinary envy-freeness, while providing the stronger consensus guarantee. A key ingredient is a private algorithm for multicolor discrepancy, which may be of independent interest. Our algorithm may require exponential time. We also obtain substantially stronger guarantees under additional structure: when all item values belong to a public alphabet of size $D$, we give a polynomial-time entry-private algorithm achieving ordinary envy-freeness up to $O(\operatorname{polylog}(mD))$ goods with high probability. Finally, we prove an $Ω(\log n)$ lower bound on the number of goods that must be removed to achieve ordinary envy-freeness under entry privacy, for sufficiently many goods, even with binary utilities.
