M. Abolhassani, S. Ehsani, Hossein Esfandiari, M. Hajiaghayi, Robert D. Kleinberg, Brendan Lucier
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引用次数: 76
Abstract
Hill and Kertz studied the prophet inequality on iid distributions [The Annals of Probability 1982]. They proved a theoretical bound of 1 - 1/e on the approximation factor of their algorithm. They conjectured that the best approximation factor for arbitrarily large n is 1/1+1/e ≃ 0.731. This conjecture remained open prior to this paper for over 30 years. In this paper we present a threshold-based algorithm for the prophet inequality with n iid distributions. Using a nontrivial and novel approach we show that our algorithm is a 0.738-approximation algorithm. By beating the bound of 1/1+1/e, this refutes the conjecture of Hill and Kertz. Moreover, we generalize our results to non-uniform distributions and discuss its applications in mechanism design.
Hill和Kertz研究了iid分布上的先知不等式[the Annals of Probability 1982]。他们证明了他们的算法的近似因子的理论边界为1 - 1/e。他们推测任意大n的最佳近似因子是1/1+1/e≃0.731。在这篇论文发表之前,这个猜想已经存在了30多年。本文提出了一种基于阈值的n - id分布的预测不等式算法。使用一种非平凡的新颖方法,我们证明了我们的算法是0.738近似算法。通过突破1/1+1/e的界限,反驳了Hill和Kertz的猜想。此外,我们将结果推广到非均匀分布,并讨论了其在机构设计中的应用。