Quantitative stability analysis for minimax distributionally robust risk optimization
Quantitative stability analysis for minimax distributionally robust risk optimization
This paper considers distributionally robust formulations of a two stage stochastic programmingproblem with the objective of minimizing a distortion risk of the minimal cost incurred at the second stage.We carry out a stability analysis by looking into variations of the ambiguity set under the Wasserstein metric,decision spaces at both stages and the support set of the random variables. In the case when the risk measureis risk neutral, the stability result is presented with the variation of the ambiguity set being measured bygeneric metrics of -structure, which provides a unified framework for quantitative stability analysis under various metrics including total variation metric and Kantorovich metric. When the ambiguity set is structured by a zeta-ball, we find that the Hausdorff distance between two -balls is bounded by the distance of their centers and difference of their radii. The findings allow us to strengthen some recent convergence results on distributionally robust optimization where the center of the Wasserstein ball is constructed by the empirical probability distribution.
Pichler, Alois
78070747-244a-48df-a775-7b1a46fe7b14
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Pichler, Alois
78070747-244a-48df-a775-7b1a46fe7b14
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Pichler, Alois and Xu, Huifu
(2018)
Quantitative stability analysis for minimax distributionally robust risk optimization.
Mathematical Programming.
(doi:10.1007/s10107-018-1347-4).
Abstract
This paper considers distributionally robust formulations of a two stage stochastic programmingproblem with the objective of minimizing a distortion risk of the minimal cost incurred at the second stage.We carry out a stability analysis by looking into variations of the ambiguity set under the Wasserstein metric,decision spaces at both stages and the support set of the random variables. In the case when the risk measureis risk neutral, the stability result is presented with the variation of the ambiguity set being measured bygeneric metrics of -structure, which provides a unified framework for quantitative stability analysis under various metrics including total variation metric and Kantorovich metric. When the ambiguity set is structured by a zeta-ball, we find that the Hausdorff distance between two -balls is bounded by the distance of their centers and difference of their radii. The findings allow us to strengthen some recent convergence results on distributionally robust optimization where the center of the Wasserstein ball is constructed by the empirical probability distribution.
Text
Pichler-Xu-MPB
- Accepted Manuscript
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Accepted/In Press date: 27 October 2018
e-pub ahead of print date: 3 November 2018
Identifiers
Local EPrints ID: 425755
URI: http://eprints.soton.ac.uk/id/eprint/425755
ISSN: 0025-5610
PURE UUID: 807db0eb-6243-4e3b-9eee-fa0526f25b61
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Date deposited: 02 Nov 2018 17:30
Last modified: 16 Mar 2024 07:13
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Author:
Alois Pichler
Author:
Huifu Xu
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