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Secretaries with Advice

Authors:

Silvio Lattanzi,

Renato Paes Leme,

Sergei VassilvitskiiAuthors Info & Claims

EC '21: Proceedings of the 22nd ACM Conference on Economics and Computation

Pages 409 - 429

https://doi.org/10.1145/3465456.3467623

Published: 18 July 2021 Publication History

Abstract

The secretary problem is probably the purest model of decision making under uncertainty. In this paper we ask which advice can we 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, to more modern versions of advice in the form of samples, to an ML-inspired model where a classifier gives us noisy signal about whether or not the current secretary is the best on the market.

Our main technique is a factor revealing LP that captures all of the problems above. 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 a new noisy binary advice model.

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Cited By

Choo DGouleakis TLing CBhattacharyya ASalakhutdinov RKolter ZHeller KWeller AOliver NScarlett JBerkenkamp F(2024)Online bipartite matching with imperfect adviceProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692420(8762-8781)Online publication date: 21-Jul-2024
https://dl.acm.org/doi/10.5555/3692070.3692420
Benomar ZPerchet VSalakhutdinov RKolter ZHeller KWeller AOliver NScarlett JBerkenkamp F(2024)Non-clairvoyant scheduling with partial predictionsProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692210(3506-3538)Online publication date: 21-Jul-2024
https://dl.acm.org/doi/10.5555/3692070.3692210
Balcan MDeBlasio DDick TKingsford CSandholm TVitercik E(2024)How Much Data Is Sufficient to Learn High-Performing Algorithms?Journal of the ACM10.1145/3676278Online publication date: 29-Jul-2024
https://doi.org/10.1145/3676278
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Index Terms

Secretaries with Advice
1. Theory of computation
  1. Design and analysis of algorithms
    1. Online algorithms

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Published In

cover image ACM Conferences

EC '21: Proceedings of the 22nd ACM Conference on Economics and Computation

July 2021

950 pages

ISBN:9781450385541

DOI:10.1145/3465456

General Chair:
Péter Biró
Hungarian Academy of Sciences
,
Program Chairs:
Shuchi Chawla
University of Wisconsin-Madison and University of Texas at Austin
,
Federico Echenique
California Institute of Technology

Copyright © 2021 Owner/Author.

This work is licensed under a Creative Commons Attribution International 4.0 License.

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SIGecom: Special Interest Group on Economics and Computation

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 18 July 2021

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EC '21

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SIGecom

EC '21: The 22nd ACM Conference on Economics and Computation

July 18 - 23, 2021

Budapest, Hungary

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Overall Acceptance Rate 664 of 2,389 submissions, 28%

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EC '25

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The 25th ACM Conference on Economics and Computation

July 7 - 11, 2025

Stanford , CA , USA

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Cited By

Choo DGouleakis TLing CBhattacharyya ASalakhutdinov RKolter ZHeller KWeller AOliver NScarlett JBerkenkamp F(2024)Online bipartite matching with imperfect adviceProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692420(8762-8781)Online publication date: 21-Jul-2024
https://dl.acm.org/doi/10.5555/3692070.3692420
Benomar ZPerchet VSalakhutdinov RKolter ZHeller KWeller AOliver NScarlett JBerkenkamp F(2024)Non-clairvoyant scheduling with partial predictionsProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692210(3506-3538)Online publication date: 21-Jul-2024
https://dl.acm.org/doi/10.5555/3692070.3692210
Balcan MDeBlasio DDick TKingsford CSandholm TVitercik E(2024)How Much Data Is Sufficient to Learn High-Performing Algorithms?Journal of the ACM10.1145/3676278Online publication date: 29-Jul-2024
https://doi.org/10.1145/3676278
Lee RSun BHajiesmaili MLui J(2024)Online Search with Predictions: Pareto-optimal Algorithm and its Applications in Energy MarketsProceedings of the 15th ACM International Conference on Future and Sustainable Energy Systems10.1145/3632775.3639590(386-407)Online publication date: 4-Jun-2024
https://dl.acm.org/doi/10.1145/3632775.3639590
Zhao TLi WZomaya A(2024)Learning-Augmented SchedulingIEEE Transactions on Computers10.1109/TC.2024.344185673:11(2548-2562)Online publication date: 1-Nov-2024
https://dl.acm.org/doi/10.1109/TC.2024.3441856
Rutten DChristianson NMukherjee DWierman A(2023)Smoothed Online Optimization with Unreliable PredictionsProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/35794427:1(1-36)Online publication date: 2-Mar-2023
https://dl.acm.org/doi/10.1145/3579442
Gravin NSun ETang Z(2023)Online Ordinal Problems: Optimality of Comparison-based Algorithms and their Cardinal Complexity2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00113(1863-1876)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00113
Moustakides GLiu XMilenkovic O(2023)Optimal stopping methodology for the secretary problem with random queriesJournal of Applied Probability10.1017/jpr.2023.6161:2(578-602)Online publication date: 2-Oct-2023
https://doi.org/10.1017/jpr.2023.61
Antoniadis AGouleakis TKleer PKolev P(2023)Secretary and online matching problems with machine learned adviceDiscrete Optimization10.1016/j.disopt.2023.10077848:P2Online publication date: 1-May-2023
https://dl.acm.org/doi/10.1016/j.disopt.2023.100778
Mitzenmacher MVassilvitskii S(2022)Algorithms with predictionsCommunications of the ACM10.1145/352808765:7(33-35)Online publication date: 21-Jun-2022
https://dl.acm.org/doi/10.1145/3528087
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