Fast Rates for Contextual Linear Optimization
This work addresses decision-making efficiency in machine learning for practitioners, though it is incremental as it refines existing methods rather than introducing a new paradigm.
The paper tackles the problem of contextual linear optimization by comparing plug-in methods with integrated estimation-optimization approaches, showing that the naive plug-in approach achieves significantly faster regret convergence rates, with specific instances avoiding near-dual-degeneracy issues.
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.