Fast Rates for Contextual Linear Optimization

• 成果类型: Article
• 署名作者: Hu, Yichun; Kallus, Nathan; Mao, Xiaojie
• 署名单位: Cornell University; Cornell University; Tsinghua University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2022.4383
• 发表日期: 2022
• 页码: 4236-4245
• 关键词: contextual stochastic optimization; personalized decision making; end-to-end optimization; estimate and then optimize

摘要

Incorporating side observations in decision making can reduce uncertainty and boost performance, but it also requires that we tackle a potentially complex predictive relationship. Although one may use off-the-shelf machine learning methods to separately learn a predictive model and plug it in, a variety of recent methods instead integrate estimation and optimization by fitting the model to directly optimize downstream decision performance. Surprisingly, in the case of contextual linear optimization, we show that the naive plug-in approach actually achieves regret convergence rates that are significantly faster than methods that directly optimize downstream decision performance. We show this by leveraging the fact that specific problem instances do not have arbitrarily bad near-dual-degeneracy. Although there are other pros and cons to consider as we discuss and illustrate numerically, our results highlight a nuanced landscape for the enterprise to integrate estimation and optimization. Our results are overall positive for practice: predictive models are easy and fast to train using existing tools; simple to interpret; and, as we show, lead to decisions that perform very well.