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Data-driven stochastic optimization for distributional ambiguity with integrated confidence region

Rebennack, S. 1
1 Institut für Operations Research (IOR), Karlsruher Institut für Technologie (KIT)

Abstract:

We discuss stochastic optimization problems under distributional ambiguity. The distributional uncertainty is captured by considering an entire family of distributions. Because we assume the existence of data, we can consider confidence regions for the different estimators of the parameters of the distributions. Based on the definition of an appropriate estimator in the interior of the resulting confidence region, we propose a new data-driven stochastic optimization problem. This new approach applies the idea of a-posteriori Bayesian methods to the confidence region. We are able to prove that the expected value, over all observations and all possible distributions, of the optimal objective function of the proposed stochastic optimization problem is bounded by a constant. This constant is small for a sufficiently large i.i.d. sample size and depends on the chosen confidence level and the size of the confidence region. We demonstrate the utility of the new optimization approach on a Newsvendor and a reliability problem.


Verlagsausgabe §
DOI: 10.5445/IR/1000143788
Veröffentlicht am 19.03.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Operations Research (IOR)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2022
Sprache Englisch
Identifikator ISSN: 0925-5001, 1573-2916
KITopen-ID: 1000143788
Erschienen in Journal of Global Optimization
Verlag Springer
Band 84
Heft 2
Seiten 255–293
Vorab online veröffentlicht am 21.01.2022
Nachgewiesen in Dimensions
Web of Science
Scopus
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