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Worst-case sensitivity

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  • Jun-ya Gotoh
  • Michael Jong Kim
  • Andrew E. B. Lim

Abstract

We introduce the notion of Worst-Case Sensitivity, defined as the worst-case rate of increase in the expected cost of a Distributionally Robust Optimization (DRO) model when the size of the uncertainty set vanishes. We show that worst-case sensitivity is a Generalized Measure of Deviation and that a large class of DRO models are essentially mean-(worst-case) sensitivity problems when uncertainty sets are small, unifying recent results on the relationship between DRO and regularized empirical optimization with worst-case sensitivity playing the role of the regularizer. More generally, DRO solutions can be sensitive to the family and size of the uncertainty set, and reflect the properties of its worst-case sensitivity. We derive closed-form expressions of worst-case sensitivity for well known uncertainty sets including smooth $\phi$-divergence, total variation, "budgeted" uncertainty sets, uncertainty sets corresponding to a convex combination of expected value and CVaR, and the Wasserstein metric. These can be used to select the uncertainty set and its size for a given application.

Suggested Citation

  • Jun-ya Gotoh & Michael Jong Kim & Andrew E. B. Lim, 2020. "Worst-case sensitivity," Papers 2010.10794, arXiv.org.
    • Handle: RePEc:arx:papers:2010.10794
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    References listed on IDEAS

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    1. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    2. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    3. Bertsimas, Dimitris & Copenhaver, Martin S., 2018. "Characterization of the equivalence of robustification and regularization in linear and matrix regression," European Journal of Operational Research, Elsevier, vol. 270(3), pages 931-942.
    4. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    5. Andrew E. B. Lim & J. George Shanthikumar, 2007. "Relative Entropy, Exponential Utility, and Robust Dynamic Pricing," Operations Research, INFORMS, vol. 55(2), pages 198-214, April.
    6. Rahimian, Hamed & Bayraksan, Güzin & Homem-de-Mello, Tito, 2019. "Controlling risk and demand ambiguity in newsvendor models," European Journal of Operational Research, Elsevier, vol. 279(3), pages 854-868.
    7. Jun-Ya Gotoh & Michael Jong Kim & Andrew E. B. Lim, 2017. "Calibration of Distributionally Robust Empirical Optimization Models," Papers 1711.06565, arXiv.org, revised May 2020.
    8. Gotoh, Jun-ya & Takano, Yuichi, 2007. "Newsvendor solutions via conditional value-at-risk minimization," European Journal of Operational Research, Elsevier, vol. 179(1), pages 80-96, May.
    9. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    10. Henry Lam, 2016. "Robust Sensitivity Analysis for Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1248-1275, November.
    11. Rockafellar, R.T. & Royset, J.O. & Miranda, S.I., 2014. "Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk," European Journal of Operational Research, Elsevier, vol. 234(1), pages 140-154.
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    Cited by:

    1. Emerson Melo, 2022. "On The Distributional Robustness Of Finite Rational Inattention Models," CAEPR Working Papers 2022-011 Classification-D, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    2. Emerson Melo, 2022. "On the Distributional Robustness of Finite Rational Inattention Models," Papers 2208.03370, arXiv.org, revised May 2023.

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