需求不确定条件下资源配置的公平与利用
Fairness and Utilization in Allocating Resources with Uncertain Demand
摘要：
资源分配问题是评价算法公平性的一个基本领域。公平性和利用率之间的权衡在这一领域有着悠久的历史。最近的一系列工作已经考虑了当对资源的需求分布在多个组中并且从概率分布中得出时的资源分配的公平性问题。在这种情况下，自然公平的要求是，来自不同群体的个人应该有（近似）相等的概率接收资源。在这一领域的一个很大程度上悬而未决的问题是限制资源的最大可能利用率和服从于这一公平条件的最大可能利用率之间的差距。在这里，我们得到了一些第一个可证明的上界这个差距。我们得到了一个任意分布的上限，以及更强的上限为特定的家庭的分布，通常用于模型的需求水平。特别是，我们发现-有点令人惊讶-有自然的分布族（包括指数和威布尔）的差距是不存在的：它是可能的，同时实现最大利用率和给定的公平概念。最后，我们表明，对于幂律分布，解之间存在非平凡的间隙，但这个间隙可以由与分布参数无关的常数因子来限制。
英文摘要：
Resource allocation problems are a fundamental domain in which to evaluate the fairness properties of algorithms. The trade-offs between fairness and utilization have a long history in this domain. A recent line of work has considered fairness questions for resource allocation when the demands for the resource are distributed across multiple groups and drawn from probability distributions. In such cases, a natural fairness requirement is that individuals from different groups should have (approximately) equal probabilities of receiving the resource. A largely open question in this area has been to bound the gap between the maximum possible utilization of the resource and the maximum possible utilization subject to this fairness condition. Here, we obtain some of the first provable upper bounds on this gap. We obtain an upper bound for arbitrary distributions, as well as much stronger upper bounds for specific families of distributions that are typically used to model levels of demand. In particular, we find - somewhat surprisingly - that there are natural families of distributions (including Exponential and Weibull) for which the gap is non-existent: it is possible to simultaneously achieve maximum utilization and the given notion of fairness. Finally, we show that for power-law distributions, there is a non-trivial gap between the solutions, but this gap can be bounded by a constant factor independent of the parameters of the distribution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
