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

Steffen Rebennack ()
Additional contact information
Steffen Rebennack: Karlsruhe Institute of Technology (KIT)

Journal of Global Optimization, 2022, vol. 84, issue 2, No 1, 255-293

Abstract: 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.

Keywords: Data-driven stochastic optimization; Bayesian approach; Distributional ambiguity; Distributionally robust stochastic optimization; Newsvendor problem (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10898-022-01146-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:84:y:2022:i:2:d:10.1007_s10898-022-01146-y

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-022-01146-y

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().