The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values are provided in advance. We propose an algorithm that achieves a nearly optimal value if the predictions are accurate and results in a constant-factor competitive ratio otherwise. We also show that the worst-case competitive ratio of an algorithm cannot be higher than some constant $< 1/\mathrm{e}$, which is the best possible competitive ratio when we ignore predictions, if the algorithm performs nearly optimally when the predictions are accurate. Additionally, for the multiple-choice secretary problem, we propose an algorithm with a similar theoretical guarantee. We empirically illustrate that if the predictions are accurate, the proposed algorithms perform well; meanwhile, if the predictions are inaccurate, performance is comparable to existing algorithms that do not use predictions.

翻译：秘书问题的价值最大化版本是从随机排序的候选者序列中雇佣价值最大的候选者的问题。本文考虑了一种场景，其中候选者价值的预测是提前提供的。我们提出了一种算法，当预测准确时，该算法能实现接近最优的价值，否则能保证恒定比的竞争性能。我们还证明，如果算法在预测准确时能近乎最优地运行，那么该算法的最坏情况竞争比不能超过某个常数$< 1/\mathrm{e}$，这是忽略预测时能达到的最佳竞争比。此外，对于多选秘书问题，我们提出了一种具有类似理论保证的算法。我们通过实验表明，当预测准确时，所提出的算法表现良好；而预测不准确时，其性能与不使用预测的现有算法相当。