A stability result for linear Markovian stochastic optimization problems

• 成果类型: Article
• 署名作者: Kiszka, Adriana; Wozabal, David
• 署名单位: Technical University of Munich
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01573-3
• 发表日期: 2022
• 页码: 871-906
• 关键词: finite-state approximations; epi-convergent discretizations; decision-processes; quantization algorithm; scenario reduction; systems; generation; trees

摘要

In this paper, we propose a semi-metric for Markov processes that allows to bound optimal values of linear Markovian stochastic optimization problems. Similar to existing notions of distance for general stochastic processes, our distance is based on transportation metrics. As opposed to the extant literature, the proposed distance is problem specific, i.e., dependent on the data of the problem whose objective value we want to bound. As a result, we are able to consider problems with randomness in the constraints as well as in the objective function and therefore relax an assumption in the extant literature. We derive several properties of the proposed semi-metric and demonstrate its use in a stylized numerical example.