Decision-Dependent Distributionally Robust Optimization with Application to Dynamic Pricing

Chengrui Qu; Huiwen Jia; Pengcheng You

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arXiv · 2508.06965

Decision-Dependent Distributionally Robust Optimization with Application to Dynamic Pricing

Chengrui Qu·Huiwen Jia·Pengcheng You

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Abstract

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.

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BibTeX RIS

Chengrui Qu, Huiwen Jia, Pengcheng You. 2025-08-09. Decision-Dependent Distributionally Robust Optimization with Application to Dynamic Pricing. https://arxiv.org/abs/2508.06965

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