  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.
