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Maximizing Sequence-Submodular Functions and Its Application to Online Advertising

Author

Listed:
  • Saeed Alaei

    (Google Research, Mountain View, California 94043)

  • Ali Makhdoumi

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Azarakhsh Malekian

    (Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada)

Abstract

Motivated by applications in online advertising, we consider a class of maximization problems where the objective is a function of the sequence of actions and the running duration of each action. For these problems, we introduce the concepts of sequence-submodularity and sequence-monotonicity , which extend the notions of submodularity and monotonicity from functions defined over sets to functions defined over sequences. We establish that if the objective function is sequence-submodular and sequence-nondecreasing, then there exists a greedy algorithm that achieves 1 − 1 / e of the optimal solution. We apply our algorithm and analysis to two applications in online advertising: online ad allocation and query rewriting. We first show that both problems can be formulated as maximizing nondecreasing sequence-submodular functions. We then apply our framework to these two problems, leading to simple greedy approaches with guaranteed performances. In particular, for the online ad allocation problem, the performance of our algorithm is 1 − 1 / e , which matches the best known existing performance, and for the query rewriting problem, the performance of our algorithm is 1 − 1 / e 1 − 1 / e , which improves on the best known existing performance in the literature.

Suggested Citation

  • Saeed Alaei & Ali Makhdoumi & Azarakhsh Malekian, 2021. "Maximizing Sequence-Submodular Functions and Its Application to Online Advertising," Management Science, INFORMS, vol. 67(10), pages 6030-6054, October.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:10:p:6030-6054
    DOI: 10.1287/mnsc.2020.3820
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    References listed on IDEAS

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    1. G. L. Nemhauser & L. A. Wolsey, 1978. "Best Algorithms for Approximating the Maximum of a Submodular Set Function," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 177-188, August.
    2. Santiago R. Balseiro & Ozan Candogan, 2017. "Optimal Contracts for Intermediaries in Online Advertising," Operations Research, INFORMS, vol. 65(4), pages 878-896, August.
    3. Nemhauser, G.L. & Wolsey, L.A., 1978. "Best algorithms for approximating the maximum of a submodular set function," LIDAM Reprints CORE 343, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. WOLSEY, Laurence A., 1982. "Maximising real-valued submodular functions: primal and dual heuristics for location problems," LIDAM Reprints CORE 486, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Lehmann, Benny & Lehmann, Daniel & Nisan, Noam, 2006. "Combinatorial auctions with decreasing marginal utilities," Games and Economic Behavior, Elsevier, vol. 55(2), pages 270-296, May.
    8. Laurence A. Wolsey, 1982. "Maximising Real-Valued Submodular Functions: Primal and Dual Heuristics for Location Problems," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 410-425, August.
    9. Arash Asadpour & Xuan Wang & Jiawei Zhang, 2020. "Online Resource Allocation with Limited Flexibility," Management Science, INFORMS, vol. 66(2), pages 642-666, February.
    10. Marek Adamczyk & Maxim Sviridenko & Justin Ward, 2016. "Submodular Stochastic Probing on Matroids," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1022-1038, August.
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    Cited by:

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