Effective Scenarios in Multistage Distributionally Robust Optimization with a Focus on Total Variation Distance
Effective Scenarios in Multistage Distributionally Robust Optimization with a Focus on Total Variation Distance
复制标题
以总变异距离为重点的多级分布鲁棒优化的有效场景
DOI：
10.1137/21m1446484
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Tito Homem
中科院分区：
文献类型：
--
作者：
Hamed Rahimian;G. Bayraksan;Tito Homem
我们研究了多阶段分布稳健优化(DRO)，以避免在量化问题潜在不确定性时的模糊性。认识到并不是所有的实现和场景路径都可能对最优值产生影响，我们研究了如何定义和识别嵌套多阶段DRO问题的关键场景的问题。我们的分析扩展了Rahimian，Bayraksan和Homem-de-Mello[Math.程序。173(1--2)：393-430,2019年]，这是在静态/两阶段设置的背景下，到多阶段设置。为此，对于一类一般的多阶段DRO问题，我们定义了情景路径的有效性和沿着情景路径实现的条件有效性的概念。当分布模糊度通过总变异距离建模时，我们提出了易于检验的条件来识别多阶段环境中情景路径的有效性。数值结果表明，这些概念对问题的潜在不确定性提供了有用的见解。
We study multistage distributionally robust optimization (DRO) to hedge against ambiguity in quantifying the underlying uncertainty of a problem. Recognizing that not all the realizations and scenario paths might have an"effect"on the optimal value, we investigate the question of how to define and identify critical scenarios for nested multistage DRO problems. Our analysis extends the work of Rahimian, Bayraksan, and Homem-de-Mello [Math. Program. 173(1--2): 393--430, 2019], which was in the context of a static/two-stage setting, to the multistage setting. To this end, we define the notions of effectiveness of scenario paths and the conditional effectiveness of realizations along a scenario path for a general class of multistage DRO problems. We then propose easy-to-check conditions to identify the effectiveness of scenario paths in the multistage setting when the distributional ambiguity is modeled via the total variation distance. Numerical results show that these notions provide useful insight on the underlying uncertainty of the problem.
问题驱动的场景生成：带有尾部风险度量的随机程序的分析方法
DOI：
10.48550/arxiv.1511.03074
发表时间：
2015
期刊：
arXiv e-prints
影响因子：
--
作者：
Fairbrother Jamie
通讯作者：
Fairbrother Jamie