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Fast Rates for Contextual Linear Optimization

Author

Listed:
  • Yichun Hu

    (School of Operations Research and Information Engineering and Cornell Tech, Cornell University, New York, New York 10044)

  • Nathan Kallus

    (School of Operations Research and Information Engineering and Cornell Tech, Cornell University, New York, New York 10044)

  • Xiaojie Mao

    (School of Economics and Management, Tsinghua University, Beijing 100084, China)

Abstract

Incorporating side observations in decision making can reduce uncertainty and boost performance, but it also requires that we tackle a potentially complex predictive relationship. Although one may use off-the-shelf machine learning methods to separately learn a predictive model and plug it in, a variety of recent methods instead integrate estimation and optimization by fitting the model to directly optimize downstream decision performance. Surprisingly, in the case of contextual linear optimization, we show that the naïve plug-in approach actually achieves regret convergence rates that are significantly faster than methods that directly optimize downstream decision performance. We show this by leveraging the fact that specific problem instances do not have arbitrarily bad near-dual-degeneracy. Although there are other pros and cons to consider as we discuss and illustrate numerically, our results highlight a nuanced landscape for the enterprise to integrate estimation and optimization. Our results are overall positive for practice: predictive models are easy and fast to train using existing tools; simple to interpret; and, as we show, lead to decisions that perform very well.

Suggested Citation

  • Yichun Hu & Nathan Kallus & Xiaojie Mao, 2022. "Fast Rates for Contextual Linear Optimization," Management Science, INFORMS, vol. 68(6), pages 4236-4245, June.
  • Handle: RePEc:inm:ormnsc:v:68:y:2022:i:6:p:4236-4245
    DOI: 10.1287/mnsc.2022.4383
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    References listed on IDEAS

    as
    1. Hamsa Bastani & Mohsen Bayati, 2020. "Online Decision Making with High-Dimensional Covariates," Operations Research, INFORMS, vol. 68(1), pages 276-294, January.
    2. Gah-Yi Ban & Cynthia Rudin, 2019. "The Big Data Newsvendor: Practical Insights from Machine Learning," Operations Research, INFORMS, vol. 67(1), pages 90-108, January.
    3. Dimitris Bertsimas & Nathan Kallus, 2020. "From Predictive to Prescriptive Analytics," Management Science, INFORMS, vol. 66(3), pages 1025-1044, March.
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    Cited by:

    1. Pan Zhao & Yifan Cui, 2023. "A Semiparametric Instrumented Difference-in-Differences Approach to Policy Learning," Papers 2310.09545, arXiv.org.
    2. Nathan Kallus & Xiaojie Mao, 2023. "Stochastic Optimization Forests," Management Science, INFORMS, vol. 69(4), pages 1975-1994, April.

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