تقرير
Data-driven Multistage Distributionally Robust Linear Optimization with Nested Distance
| العنوان: | Data-driven Multistage Distributionally Robust Linear Optimization with Nested Distance |
|---|---|
| المؤلفون: | Gao, Rui, Arora, Rohit, Huang, Yizhe |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Computer Science - Machine Learning, Mathematics - Probability, Statistics - Machine Learning |
| الوصف: | We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to solve due to its inherent non-convexity. In this paper, we demonstrate that, under mild conditions, the robust risk evaluation of a given policy can be expressed in an equivalent recursive form. Furthermore, assuming stagewise independence, we derive equivalent dynamic programming reformulations to find an optimal robust policy that is time-consistent and well-defined on unseen sample paths. Our reformulations reconcile two modeling frameworks: the multistage-static formulation (with nested distance) and the multistage-dynamic formulation (with one-period Wasserstein distance). Moreover, we identify tractable cases when the value functions can be computed efficiently using convex optimization techniques. Comment: First appeared online at https://optimization-online.org/?p=20641 on Oct 15, 2022 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.16346 |
| رقم الأكسشن: | edsarx.2407.16346 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |