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.

翻译：候选人按顺序到达面试流程，并依据其相对于前任的排名进行评估。基于每个时刻可获得的排名信息，需要设计一个决策机制，以在当前候选人中选择或拒绝，从而最大化选中最佳候选人的概率。这一经典版本的“秘书问题”已通过组合数学方法及众多变体形式得到深入研究。本文考虑一种新的特定版本，其中在审查过程中允许询问外部专家，以提高做出正确决策的概率。与现有公式不同，我们考虑的专家并非绝对可靠，可能提供有缺陷的建议。针对该问题的求解，我们采用概率方法，将查询时间视为连续停止时间，并借助最优停止理论对其进行优化。对于每个查询时间，我们还需设计一种机制，以决定是否应在该查询时刻终止搜索。在通常假设专家绝对可靠的情况下，该决策是直接的，但当专家存在缺陷时，其结构则复杂得多。