论文标题
关于$ 1/e $ -Strategy的最佳选择的公开问题的答案
Answer to an open question concerning the $1/e$-strategy for best choice under no information
论文作者
论文摘要
本文回答了一个关于最佳选择问题的$ 1/e $ strategy的长期开放问题。 $ n $候选工作有时会独立地分配给$ [0,1] $。面试官知道每个候选人如何相对于到目前为止所看到的所有其他候选人的排名，并且必须立即任命或拒绝每个候选人到达。目的是选择最好的整体。 $ 1/e $的策略是遵循以下规则：“直到时间$ 1/e $，然后任命到目前为止最好的候选人（如果有）。” 这个问题于1983年首次与拉里·谢普（Larry Shepp）讨论，是要知道，如果没有“有关选项总数的信息”，那么$ 1/e $ sTrategy是否是最佳的。这可能是对各种解释开放的，但是我们将采用\ cite {by}的比例提示过程。这种过程被证明具有非常刚性的结构，是时间变化的{\ em纯出生过程}，这允许一些精确的分布计算，我们从中推断出$ 1/e $ strategy实际上并不是最佳的。
This paper answers a long-standing open question concerning the $1/e$-strategy for the problem of best choice. $N$ candidates for a job arrive at times independently uniformly distributed in $[0,1]$. The interviewer knows how each candidate ranks relative to all others seen so far, and must immediately appoint or reject each candidate as they arrive. The aim is to choose the best overall. The $1/e$ strategy is to follow the rule: `Do nothing until time $1/e$, then appoint the first candidate thereafter who is best so far (if any).' The question, first discussed with Larry Shepp in 1983, was to know whether the $1/e$-strategy is optimal if one has `no information about the total number of options'. Quite what this might mean is open to various interpretations, but we shall take the proportional-increment process formulation of \cite{BY}. Such processes are shown to have a very rigid structure, being time-changed {\em pure birth processes}, and this allows some precise distributional calculations, from which we deduce that the $1/e$-strategy is in fact not optimal.
