候選人按順序進入面試程式，這導緻他們會被相對于他們的前任排名。根據每次可用的級别，必須開發一種選擇或解雇目前候選人的決策機制，以最大限度地提高選擇最佳人選的機會。這個經典版本的“秘書問題”已經被深入研究，主要使用組合方法，以及許多其他變體。在這項工作中，我們考慮一個特殊的新版本，在審查期間允許向外部專家查詢，以提高做出正确決策的機率。與現有的公式不同，我們認為專家不一定是絕對正确的，可能提供的建議可能是錯誤的。為了解決我們的問題，我們采用了一個機率的方法，并将查詢次數視為連續的停止時間，我們利用最優停止理論優化。對于每個查詢時間，我們還必須設計一種機制來決定是否在查詢時間終止搜尋。根據正确率較高的專家的通常假設，這個決定很簡單，但當專家有錯誤時，它的結構就複雜得多了。
原文标題: Optimal stopping methodology for the secretary problem with random queries
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.
随機查詢“秘書問題”的最優停止方法.pdf