Fast Rates for Contextual Linear Optimization

Yichun Hu (), Nathan Kallus () and Xiaojie Mao ()
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Yichun Hu: School of Operations Research and Information Engineering and Cornell Tech, Cornell University, New York, New York 10044
Nathan Kallus: School of Operations Research and Information Engineering and Cornell Tech, Cornell University, New York, New York 10044
Xiaojie Mao: School of Economics and Management, Tsinghua University, Beijing 100084, China

Management Science, 2022, vol. 68, issue 6, 4236-4245

Abstract: 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 naïve 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.

Keywords: contextual stochastic optimization; personalized decision making; end-to-end optimization; estimate and then optimize (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:68:y:2022:i:6:p:4236-4245

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