顺序公平分配:实现最优嫉妒-效率权衡曲线

Sean R. Sinclair, Siddhartha Banerjee, C. Yu
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引用次数: 23

摘要

我们考虑将有限资源分配给经过T轮到达的个人的问题。每个回合都有随机数量的个体到达,并且个体可以根据他们的类型(即对不同资源的偏好)来特征化。在这种情况下,“公平”的标准概念是,分配同时满足无嫉妒和效率。对于可分资源,当每种类型的个体数量事先已知时,上述期望可以同时实现一大类效用函数。然而,在网络环境中,当每一种类型的个人数量都是一轮一轮地显示时,没有任何策略可以同时保证这些期望。我们表明,在在线设置中,两个期望的属性(嫉妒自由和效率)是直接竞争的,因为任何达到LT因子的加法反事实嫉妒自由的算法都必然遭受至少1 / LT的效率损失。我们用一个简单的算法guard - hope补充了这种不确定性原则,该算法基于自适应阈值策略分配资源,并能够在该边界上实现任何公平-效率点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Sequential Fair Allocation: Achieving the Optimal Envy-Efficiency Tradeoff Curve
We consider the problem of dividing limited resources to individuals arriving over T rounds. Each round has a random number of individuals arrive, and individuals can be characterized by their type (i.e. preferences over the different resources). A standard notion of 'fairness' in this setting is that an allocation simultaneously satisfy envy-freeness and efficiency. For divisible resources, when the number of individuals of each type are known upfront, the above desiderata are simultaneously achievable for a large class of utility functions. However, in an online setting when the number of individuals of each type are only revealed round by round, no policy can guarantee these desiderata simultaneously. We show that in the online setting, the two desired properties (envy-freeness and efficiency) are in direct contention, in that any algorithm achieving additive counterfactual envy-freeness up to a factor of LT necessarily suffers a efficiency loss of at least 1 / LT. We complement this uncertainty principle with a simple algorithm, Guarded-Hope, which allocates resources based on an adaptive threshold policy and is able to achieve any fairness-efficiency point on this frontier.
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