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程序, 其排名与其前任相较。 根据每个时段的级别, 必须开发一种选择或解雇当前候选人的决定机制, 以便尽量扩大选择最佳候选人的机会。 这个典型的“ 秘书问题” 版本已经用多为组合式的方法以及许多其他变体来进行深入研究。 在这项工作中, 我们考虑一个特定的新版本, 允许在审查过程中询问外部专家, 以提高做出正确决定的可能性。 与现有的配方不同, 我们考虑的专家不一定不可靠, 并且可能提供错误的建议。 为了解决我们的问题, 我们采用概率性的方法, 并将询问时间视为我们利用最佳停止理论优化的连续中断时间。 对于每次询问的时间, 我们还必须设计一个机制, 来决定是否在询问时间终止搜索。 这一决定在通常的错误专家假设下是直截了当, 但当专家有错误时, 其结构就复杂得多 。