带随机查询的秘书问题的最优停止方法
Optimal Stopping Methodology for the Secretary Problem with Random Queries
AI总结：
本文研究允许向可能出错的专家进行随机查询的秘书问题变体，利用最优停止理论优化查询时刻并设计终止决策机制，以最大化选中最佳候选人的概率。
摘要：
候选人依次到达并接受面试，面试结果使其相对于先前候选人被赋予排名。基于每个时刻可获得的排名，必须设计一种决策机制来录用或淘汰当前候选人，以最大化选中最佳候选人的概率。这一经典“秘书问题”主要通过组合方法得到了深入研究，并衍生出大量其他变体。本文考虑一个特定的新版本：在审阅过程中允许向外部专家进行查询，以提高做出正确决策的概率。与现有表述不同，我们考虑的专家并非绝对可靠，其提供的建议可能存在错误。为求解该问题，我们采用概率方法，将查询时刻视为连续的最优停止时刻，并借助最优停止理论对其进行优化。对于每个查询时刻，还必须设计一种机制来决定是否应在该查询时刻终止搜索。在专家绝对可靠的通常假设下，这一决策是直接的；但当专家可能出错时，其结构要复杂得多。
英文摘要：
Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, one must develop a decision mechanism that selects or dismisses the current candidate in an effort to maximize the chance to select the best. This classical version of the ``Secretary problem'' has been studied in depth using mostly combinatorial approaches, along with numerous other variants. In this work we consider a particular new version where during reviewing one is allowed to query an external expert to improve the probability of making the correct decision. Unlike existing formulations, we consider experts that are not necessarily infallible and may provide suggestions that can be faulty. For the solution of our problem we adopt a probabilistic methodology and view the querying times as consecutive stopping times which we optimize with the help of optimal stopping theory. For each querying time we must also design a mechanism to decide whether we should terminate the search at the querying time or not. This decision is straightforward under the usual assumption of infallible experts but, when experts are faulty, it has a far more intricate structure.
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。
