As a famous result, the ``37\% Law'' for Secretary Problem has widely influenced peoples' perception on online decision strategies about choice. However, using this strategy, too many attractive candidates may be rejected in the first 37\%, and in practice people also tend to stop earlier\cite{Bearden_early}. In this paper, we argued that in most cases, the best-only optimization does not obtain an optimal outcome, while the optimal cutoff should be $O(\sqrt{n})$. And we also showed that in some strict objective that only cares several best candidates, $\Theta(n)$ skips are still needed.
翻译:作为著名结果,“37 ⁇ L'Law' for Secretary Problems”对在线决策策略的选择产生了广泛的影响。然而,使用这一策略,在最初37 ⁇ L(cite {Bearden_early})中,太多有吸引力的候选人可能会在最初37 ⁇ LO(Law)中被否决,而实际上人们也倾向于停止早期的\cite{Bearden_early}。在本文中,我们争论说,在多数情况下,最佳的优化不会取得最佳结果,而最佳的削减应该为$O(sqrt{n}$。 我们还表明,在某些严格的目标中,只关心几个最佳候选人,我们仍然需要$\theta(n)$。