The Secretary Problem with Predictions

Kaito Fujii () and Yuichi Yoshida ()
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Kaito Fujii: National Institute of Informatics, Tokyo 101-8430, Japan
Yuichi Yoshida: National Institute of Informatics, Tokyo 101-8430, Japan

Mathematics of Operations Research, 2024, vol. 49, issue 2, 1241-1262

Abstract: 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 / 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.

Keywords: Primary: 60G40; secondary: 90C27; learning-augmented algorithms; secretary problems; optimal stopping theory (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:2:p:1241-1262

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