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- W3136709043 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." @default.
- W3136709043 created "2021-03-29" @default.
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- W3136709043 date "2020-01-01" @default.
- W3136709043 modified "2023-09-25" @default.
- W3136709043 title "Worst-Case Sensitivity" @default.
- W3136709043 doi "https://doi.org/10.2139/ssrn.3716020" @default.
- W3136709043 hasPublicationYear "2020" @default.
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