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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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    Cited by:

    1. Emerson Melo, 2022. "On the Distributional Robustness of Finite Rational Inattention Models," Papers 2208.03370, arXiv.org, revised May 2023.
    2. 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.

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