Fast Rates for Contextual Linear Optimization

TL;DR

This paper demonstrates that in contextual linear optimization, using a simple plug-in predictive model yields faster regret convergence than more complex joint estimation-optimization methods, due to problem-specific properties.

Contribution

It reveals that the naive plug-in approach outperforms integrated methods in certain cases, challenging common assumptions in decision-optimization integration.

Findings

Plug-in approach achieves faster regret convergence.

Specific problem instances lack severe near-dual-degeneracy.

Predictive models are effective and easy to implement.

Abstract

Incorporating side observations in decision making can reduce uncertainty and boost performance, but it also requires we tackle a potentially complex predictive relationship. While 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. While 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.