计算机科学
数学优化
随机规划
随机优化
动态规划
计算
核(代数)
多样性(控制论)
班级(哲学)
度量(数据仓库)
机器学习
人工智能
算法
数据挖掘
数学
组合数学
作者
Dimitris Bertsimas,Christopher McCord,Bradley Sturt
标识
DOI:10.1016/j.ejor.2022.03.030
摘要
We develop a tractable and flexible data-driven approach for incorporating side information into multi-stage stochastic programming. The proposed framework uses predictive machine learning methods (such as k-nearest neighbors, kernel regression, and random forests) to weight the relative importance of various data-driven uncertainty sets in a robust optimization formulation. Through a novel measure concentration result for a class of supervised machine learning methods, we prove that the proposed approach is asymptotically optimal for multi-period stochastic programming with side information. We also describe a general-purpose approximation for these optimization problems, based on overlapping linear decision rules, which is computationally tractable and produces high-quality solutions for dynamic problems with many stages. Across a variety of multi-stage and single-stage examples in inventory management, finance, and shipment planning, our method achieves improvements of up to 15% over alternatives and requires less than one minute of computation time on problems with twelve stages.
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