Worst-Case Sensitivity

39 Pages Posted: 3 Dec 2020

See all articles by Jun-ya Gotoh

Jun-ya Gotoh

Chuo University - Department of Data Science for Business Innovation

Michael Jong Kim

Sauder School of Business, University of British Columbia

Andrew Lim

National University of Singapore (NUS) - Department of Decision Sciences; National University of Singapore (NUS) - Department of Finance; National University of Singapore (NUS) - Institute for Operations Research and Analytics

Date Written: October 21, 2020

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.

Keywords: Distributionally robust optimization, worst-case sensitivity, generalized measure of deviation, model uncertainty, uncertainty sets, regularizer

JEL Classification: 90C17, 90C13

Suggested Citation

Gotoh, Jun-ya and Kim, Michael Jong and Lim, Andrew E. B., Worst-Case Sensitivity (October 21, 2020). Available at SSRN: https://ssrn.com/abstract=3716020 or http://dx.doi.org/10.2139/ssrn.3716020

Jun-ya Gotoh

Chuo University - Department of Data Science for Business Innovation ( email )

1-13-27 Kasuga
Bunkyo-ku, Tokyo 112-8551
Japan
+81-3-3817-1928 (Phone)

HOME PAGE: http://www.indsys.chuo-u.ac.jp/~jgoto/

Michael Jong Kim

Sauder School of Business, University of British Columbia ( email )

Vancouver
Canada

Andrew E. B. Lim (Contact Author)

National University of Singapore (NUS) - Department of Decision Sciences ( email )

NUS Business School
Mochtar Riady Building, 15 Kent Ridge
Singapore, 119245
Singapore

National University of Singapore (NUS) - Department of Finance ( email )

Mochtar Riady Building
15 Kent Ridge Drive
Singapore, 119245
Singapore

National University of Singapore (NUS) - Institute for Operations Research and Analytics ( email )

Singapore

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
61
Abstract Views
377
rank
442,876
PlumX Metrics