Scholarlink

<p>In this paper, we solve a class of distributionally robust optimization (DRO) problems with Lipschitz continuous loss functions and weakly compact ambiguity sets via sublinear expectation introduced by Peng (2009). We reformulate the DRO problem as a minimization problem by using sublinear expectation, and introduce a discrete approximation by grouping samples. We prove that optimal values and optimal solutions of the discrete problem converge to those of the DRO problem with probability 1 under capacity. We show that the discrete form is an asymptotic unbiased estimator for the sublinear expectation of the loss function, and provide the quantification of the difference between the discrete problem and the DRO problem with a special moment ambiguity set. Numerical experiments of two real life data sets are conducted. Our preliminary numerical results show that the sublinear expectation method outperforms the existing duality method, especially from the perspective of reliability.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Solving a class of distributionally robust optimization problems with sublinear expectation

  • 期刊论文

  • 发表日期：

    2026年6月23日

查看全文
  • Xingbang Cui,
  • Xiaojun Chen

摘要

In this paper, we solve a class of distributionally robust optimization (DRO) problems with Lipschitz continuous loss functions and weakly compact ambiguity sets via sublinear expectation introduced by Peng (2009). We reformulate the DRO problem as a minimization problem by using sublinear expectation, and introduce a discrete approximation by grouping samples. We prove that optimal values and optimal solutions of the discrete problem converge to those of the DRO problem with probability 1 under capacity. We show that the discrete form is an asymptotic unbiased estimator for the sublinear expectation of the loss function, and provide the quantification of the difference between the discrete problem and the DRO problem with a special moment ambiguity set. Numerical experiments of two real life data sets are conducted. Our preliminary numerical results show that the sublinear expectation method outperforms the existing duality method, especially from the perspective of reliability.