On the Relevance of Incorporating Decision Dependence in Distributional Ambiguity
Abstract
Most existing studies on distributionally robust optimization (DRO) with a decision-dependent ambiguity set focus on the computational and theoretical challenges posed by this class of problems. In this paper, we adopt a combined modeling and computational perspective to understand the trade-offs between modeling fidelity, solution quality, and computational effort, particularly in comparison with DRO models using decision-independent ambiguity sets. Motivated by representative applications in joint pricing-stocking newsvendor problems with price-dependent demand and facility location problems with location-dependent demand, we consider a two-stage stochastic mixed-integer program with (non)convex continuous recourse. Assuming a finite sample space, we model the decision-dependent distributional ambiguity with a polyhedral ambiguity set and reformulate the problem as a nonconvex mixed-integer nonlinear program. To efficiently solve the reformulations, we propose decomposition-based cutting-plane algorithms. Our experiments on benchmark instances indicate that a decision-dependent ambiguity set substantially reduces the postdecision disappointment for the newsvendor and out-of-sample cost for the facility location problems, up to 65% and 7% on average, respectively; thereby mitigating the optimizer's curse relative to a decision-independent DRO. However, this improvement is achieved at the expense of increased computational effort, with the absolute runtime ratio falling between 2 and 25 for medium- to large-sized newsvendor instances and between 2 and 12 for facility location instances.
Related
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- Distributional Counterfactual Dependence in the Special Sciences
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- Generalized Tan-Arlery-Rabaste-Lehmann-Ovarlez Lower Bound on Ambiguity Function of a Set of Sequences With Mismatched Filters
BibTeX
@misc{rahimian2026relevance,
title = {{On the Relevance of Incorporating Decision Dependence in Distributional Ambiguity}},
author = {Hamed Rahimian and Sanjay Mehrotra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33926},
eprint = {2609.33926},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33926},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Relevance of Incorporating Decision Dependence in Distributional Ambiguity
AU - Hamed Rahimian
AU - Sanjay Mehrotra
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.33926
UR - https://arxiv.org/abs/2609.33926
AB - Most existing studies on distributionally robust optimization (DRO) with a decision-dependent ambiguity set focus on the computational and theoretical challenges posed by this class of problems. In this paper, we adopt a combined modeling and computational perspective to understand the trade-offs between modeling fidelity, solution quality, and computational effort, particularly in comparison with DRO models using decision-independent ambiguity sets. Motivated by representative applications in joint pricing-stocking newsvendor problems with price-dependent demand and facility location problems with location-dependent demand, we consider a two-stage stochastic mixed-integer program with (non)convex continuous recourse. Assuming a finite sample space, we model the decision-dependent distributional ambiguity with a polyhedral ambiguity set and reformulate the problem as a nonconvex mixed-integer nonlinear program. To efficiently solve the reformulations, we propose decomposition-based cutting-plane algorithms. Our experiments on benchmark instances indicate that a decision-dependent ambiguity set substantially reduces the postdecision disappointment for the newsvendor and out-of-sample cost for the facility location problems, up to 65% and 7% on average, respectively; thereby mitigating the optimizer's curse relative to a decision-independent DRO. However, this improvement is achieved at the expense of increased computational effort, with the absolute runtime ratio falling between 2 and 25 for medium- to large-sized newsvendor instances and between 2 and 12 for facility location instances.
ER -