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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2508.06965 |
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| _version_ | 1866908483664740352 |
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| author | Qu, Chengrui Jia, Huiwen You, Pengcheng |
| author_facet | Qu, Chengrui Jia, Huiwen You, Pengcheng |
| contents | We consider decision-making problems under decision-dependent uncertainty (DDU), where the distribution of uncertain parameters depends on the decision variables and is only observable through a finite offline dataset. To address this challenge, we formulate a decision-dependent distributionally robust optimization (DD-DRO) problem, and leverage multivariate interpolation techniques along with the Wasserstein metric to construct decision-dependent nominal distributions (thereby decision-dependent ambiguity sets) based on the offline data. We show that the resulting ambiguity sets provide a finite-sample, high-probability guarantee that the true decision-dependent distribution is contained within them. Furthermore, we establish key properties of the DD-DRO framework, including a non-asymptotic out-of-sample performance guarantee, an optimality gap bound, and a tractable reformulation. The practical effectiveness of our approach is demonstrated through numerical experiments on a dynamic pricing problem with nonstationary demand, where the DD-DRO solution produces pricing strategies with guaranteed expected revenue. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decision-Dependent Distributionally Robust Optimization with Application to Dynamic Pricing Qu, Chengrui Jia, Huiwen You, Pengcheng Optimization and Control We consider decision-making problems under decision-dependent uncertainty (DDU), where the distribution of uncertain parameters depends on the decision variables and is only observable through a finite offline dataset. To address this challenge, we formulate a decision-dependent distributionally robust optimization (DD-DRO) problem, and leverage multivariate interpolation techniques along with the Wasserstein metric to construct decision-dependent nominal distributions (thereby decision-dependent ambiguity sets) based on the offline data. We show that the resulting ambiguity sets provide a finite-sample, high-probability guarantee that the true decision-dependent distribution is contained within them. Furthermore, we establish key properties of the DD-DRO framework, including a non-asymptotic out-of-sample performance guarantee, an optimality gap bound, and a tractable reformulation. The practical effectiveness of our approach is demonstrated through numerical experiments on a dynamic pricing problem with nonstationary demand, where the DD-DRO solution produces pricing strategies with guaranteed expected revenue. |
| title | Decision-Dependent Distributionally Robust Optimization with Application to Dynamic Pricing |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.06965 |