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A study of data-driven distributionally robust optimization with incomplete joint data under finite support
European Journal of Operational Research ( IF 6.0 ) Pub Date : 2022-06-20 , DOI: 10.1016/j.ejor.2022.06.032
Ke Ren , Hoda Bidkhori

Missing data is a common issue for many practical data-driven stochastic programming problems. The state-of-the-art approaches first estimate the missing data values and then separately solve the corresponding stochastic programming. Accurate estimation of missing values is typically inaccessible as it requires enormous data and sophisticated statistical methods. Therefore, this paper proposes an integrated approach, a distributionally robust optimization (DRO) framework, that simultaneously tackles the missing data problem and data-driven stochastic optimization by hedging against the uncertainties of the missing values. This paper adds to the DRO literature by considering the practical scenario where the data can be incomplete and partially observable; it particularly focuses on data distributions with finite support. We construct several classes of ambiguity sets for our DRO model utilizing the incomplete data sets, maximum likelihood estimation method, and different metrics. We prove the statistical consistency and finite sample guarantees of the corresponding models and provide tractable reformulations of our model for different scenarios. We perform computational studies on the multi-item inventory control problem and portfolio optimization using synthetic and real-world data. We validate that our method outperforms the traditional estimate-then-optimized approaches.



中文翻译:

有限支持下不完整联合数据的数据驱动分布鲁棒优化研究

丢失数据是许多实际数据驱动的随机规划问题的常见问题。最先进的方法首先估计缺失的数据值,然后分别求解相应的随机规划。由于需要大量数据和复杂的统计方法,因此通常无法准确估计缺失值。因此,本文提出了一种集成方法,即分布式鲁棒优化 (DRO) 框架,通过对冲缺失值的不确定性,同时解决缺失数据问题和数据驱动的随机优化问题。本文通过考虑数据可能不完整且部分可观察的实际场景来补充 DRO 文献;它特别关注具有有限支持的数据分布。我们利用不完整的数据集、最大似然估计方法和不同的度量为我们的 DRO 模型构建了几类歧义集。我们证明了相应模型的统计一致性和有限样本保证,并为我们的模型针对不同场景提供了易于处理的重新表述。我们使用合成和真实数据对多项目库存控制问题和投资组合优化进行计算研究。我们验证我们的方法优于传统的估计然后优化的方法。我们证明了相应模型的统计一致性和有限样本保证,并为我们的模型针对不同场景提供了易于处理的重新表述。我们使用合成和真实数据对多项目库存控制问题和投资组合优化进行计算研究。我们验证我们的方法优于传统的估计然后优化的方法。我们证明了相应模型的统计一致性和有限样本保证,并为我们的模型针对不同场景提供了易于处理的重新表述。我们使用合成和真实数据对多项目库存控制问题和投资组合优化进行计算研究。我们验证我们的方法优于传统的估计然后优化的方法。

更新日期:2022-06-20
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