Smart Predict, then Optimize

• 成果类型: Article
• 署名作者: Elmachtoub, Adam N.; Grigas, Paul
• 署名单位: Columbia University; Columbia University; University of California System; University of California Berkeley
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2020.3922
• 发表日期: 2022
• 页码: 9-26
• 关键词: prescriptive analytics; Data-Driven Optimization; Machine Learning; Linear Regression

摘要

Many real-world analytics problems involve two significant challenges: prediction and optimization. Because of the typically complex nature of each challenge, the standard paradigm is predict-then-optimize. By and large, machine learning tools are intended to minimize prediction error and do not account for how the predictions will be used in the downstream optimization problem. In contrast, we propose a new and very general framework, called Smart Predict, then Optimize (SPO), which directly leverages the optimization problem structure-that is, its objective and constraints-for designing better prediction models. A key component of our framework is the SPO loss function, which measures the decision error induced by a prediction. Training a prediction model with respect to the SPO loss is computationally challenging, and, thus, we derive, using duality theory, a convex surrogate loss function, which we call the SPO+ loss. Most importantly, we prove that the SPO+ loss is statistically consistent with respect to the SPO loss under mild conditions. Our SPO+ loss function can tractably handle any polyhedral, convex, or even mixed-integer optimization problem with a linear objective. Numerical experiments on shortest-path and portfolio-optimization problems show that the SPO framework can lead to significant improvement under the predict-then-optimize paradigm, in particular, when the prediction model being trained is misspecified. We find that linear models trained using SPO+ loss tend to dominate random-forest algorithms, even when the ground truth is highly nonlinear.