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Predictive stochastic programming

Author

Listed:
  • Yunxiao Deng

    (University of Southern California)

  • Suvrajeet Sen

    (University of Southern California)

Abstract

Several emerging applications call for a fusion of statistical learning and stochastic programming (SP). We introduce a new class of models which we refer to as Predictive Stochastic Programming (PSP). Unlike ordinary SP, PSP models work with datasets which represent random covariates, often refered to as predictors (or features) and responses (or labels) in the machine learning literature. As a result, these PSP models call for methodologies which borrow relevant concepts from both learning and optimization. We refer to such a methodology as Learning Enabled Optimization (LEO). This paper sets forth the foundation for such a framework by introducing several novel concepts such as statistical optimality, hypothesis tests for model-fidelity, generalization error of PSP, and finally, a non-parametric methodology for model selection. These new concepts, which are collectively referred to as LEO, provide a formal framework for modeling, solving, validating, and reporting solutions for PSP models. We illustrate the LEO framework by applying it to a production-marketing coordination model based on combining a pedagogical production planning model with an advertising dataset intended for sales prediction.

Suggested Citation

  • Yunxiao Deng & Suvrajeet Sen, 2022. "Predictive stochastic programming," Computational Management Science, Springer, vol. 19(1), pages 65-98, January.
    • Handle: RePEc:spr:comgts:v:19:y:2022:i:1:d:10.1007_s10287-021-00400-0
    DOI: 10.1007/s10287-021-00400-0
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    References listed on IDEAS

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    1. Daniela Pucci de Farias & Benjamin Van Roy, 2004. "On Constraint Sampling in the Linear Programming Approach to Approximate Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 462-478, August.
    2. Michael Freimer & Jeffrey Linderoth & Douglas Thomas, 2012. "The impact of sampling methods on bias and variance in stochastic linear programs," Computational Optimization and Applications, Springer, vol. 51(1), pages 51-75, January.
    3. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    4. Ignacio Rios & Roger Wets & David Woodruff, 2015. "Multi-period forecasting and scenario generation with limited data," Computational Management Science, Springer, vol. 12(2), pages 267-295, April.
    5. 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.
    6. Suvrajeet Sen & Yifan Liu, 2016. "Mitigating Uncertainty via Compromise Decisions in Two-Stage Stochastic Linear Programming: Variance Reduction," Operations Research, INFORMS, vol. 64(6), pages 1422-1437, December.
    7. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    8. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, August.
    9. Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    10. Dimitris Bertsimas & Nathan Kallus, 2020. "From Predictive to Prescriptive Analytics," Management Science, INFORMS, vol. 66(3), pages 1025-1044, March.
    11. Jeff Linderoth & Alexander Shapiro & Stephen Wright, 2006. "The empirical behavior of sampling methods for stochastic programming," Annals of Operations Research, Springer, vol. 142(1), pages 215-241, February.
    12. Dimitris Bertsimas & Romy Shioda, 2007. "Classification and Regression via Integer Optimization," Operations Research, INFORMS, vol. 55(2), pages 252-271, April.
    13. Ilya O. Ryzhov & Warren B. Powell & Peter I. Frazier, 2012. "The Knowledge Gradient Algorithm for a General Class of Online Learning Problems," Operations Research, INFORMS, vol. 60(1), pages 180-195, February.
    14. Johannes O. Royset & Roberto Szechtman, 2013. "Optimal Budget Allocation for Sample Average Approximation," Operations Research, INFORMS, vol. 61(3), pages 762-776, June.
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