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Secretaries with Advice

Author

Listed:
  • Paul Dütting

    (Google Research, 8002 Zurich, Switzerland)

  • Silvio Lattanzi

    (Google Research, 8002 Zurich, Switzerland)

  • Renato Paes Leme

    (Google Research, New York, New York 10011)

  • Sergei Vassilvitskii

    (Google Research, New York, New York 10011)

Abstract

The secretary problem is probably the purest model of decision making under uncertainty. In this paper, we ask which advice we can give the algorithm to improve its success probability. We propose a general model that unifies a broad range of problems: from the classic secretary problem with no advice to the variant where the quality of a secretary is drawn from a known distribution and the algorithm learns each candidate’s quality on arrival, more modern versions of advice in the form of samples, and a machine-learning inspired model where a classifier gives us a noisy signal about whether the current secretary is the best on the market. Our main technique is a factor-revealing linear program (LP) that captures all of these problems. We use this LP formulation to gain structural insight into the optimal policy. Using tools from linear programming, we present a tight analysis of optimal algorithms for secretaries with samples, optimal algorithms when secretaries’ qualities are drawn from a known distribution, and optimal algorithms for a new noisy binary advice model.

Suggested Citation

  • Paul Dütting & Silvio Lattanzi & Renato Paes Leme & Sergei Vassilvitskii, 2024. "Secretaries with Advice," Mathematics of Operations Research, INFORMS, vol. 49(2), pages 856-879, May.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:2:p:856-879
    DOI: 10.1287/moor.2023.1384
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    References listed on IDEAS

    as
    1. Hlynka, M. & Sheahan, J. N., 1988. "The secretary problem for a random walk," Stochastic Processes and their Applications, Elsevier, vol. 28(2), pages 317-325, June.
    2. Niv Buchbinder & Kamal Jain & Mohit Singh, 2014. "Secretary Problems via Linear Programming," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 190-206, February.
    Full references (including those not matched with items on IDEAS)

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