A Predictive Prescription Using Minimum Volume k-Nearest Neighbor Enclosing Ellipsoid and Robust Optimization
A Predictive Prescription Using Minimum Volume k-Nearest Neighbor Enclosing Ellipsoid and Robust Optimization
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DOI：
10.3390/math9020119
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发表时间：
2021-01-01
期刊：
影响因子：
2.4
通讯作者：
Ohmori, Shunichi
中科院分区：
文献类型：
--
作者：
Ohmori, Shunichi
本文研究了从数据中得出决策的预测性和规范性分析框架的集成。传统上，在预测分析中，目的是使用统计和机器学习从数据中得出未知参数的预测，而在规范分析中，目的是使用优化技术从已知参数中得出决策。这些都是独立研究的，但预测分析中的预测误差对规范分析中决策的影响尚不清楚。提出了一种融合机器学习和稳健优化的建模框架。该算法利用k近邻模型，根据观测到的辅助数据来预测不确定参数的分布。包含k近邻的封闭最小体积椭球被用来形成稳健优化公式的不确定性集。对于参数不确定的两阶段线性随机规划，我们给出了数据驱动的决策框架和新的稳健性概念。该问题可以归结为一个凸规划问题，从而可以用现成的求解器非常有效地求解到最优解。
This paper studies the integration of predictive and prescriptive analytics framework for deriving decision from data. Traditionally, in predictive analytics, the purpose is to derive prediction of unknown parameters from data using statistics and machine learning, and in prescriptive analytics, the purpose is to derive a decision from known parameters using optimization technology. These have been studied independently, but the effect of the prediction error in predictive analytics on the decision-making in prescriptive analytics has not been clarified. We propose a modeling framework that integrates machine learning and robust optimization. The proposed algorithm utilizes the k-nearest neighbor model to predict the distribution of uncertain parameters based on the observed auxiliary data. The enclosing minimum volume ellipsoid that contains k-nearest neighbors of is used to form the uncertainty set for the robust optimization formulation. We illustrate the data-driven decision-making framework and our novel robustness notion on a two-stage linear stochastic programming under uncertain parameters. The problem can be reduced to a convex programming, and thus can be solved to optimality very efficiently by the off-the-shelf solvers.