  In data-driven stochastic optimization, model parameters of the underlying
distribution need to be estimated from data in addition to the optimization
task. Recent literature considers integrating the estimation and optimization
processes by selecting model parameters that lead to the best empirical
objective performance. This integrated approach, which we call
integrated-estimation-optimization (IEO), can be readily shown to outperform
simple estimate-then-optimize (ETO) when the model is misspecified. In this
paper, we show that a reverse behavior appears when the model class is
well-specified and there is sufficient data. Specifically, for a general class
of nonlinear stochastic optimization problems, we show that simple ETO
outperforms IEO asymptotically when the model class covers the ground truth, in
the strong sense of stochastic dominance of the regret. Namely, the entire
distribution of the regret, not only its mean or other moments, is always
better for ETO compared to IEO. Our results also apply to constrained,
contextual optimization problems where the decision depends on observed
features. Whenever applicable, we also demonstrate how standard sample average
approximation (SAA) performs the worst when the model class is well-specified
in terms of regret, and best when it is misspecified. Finally, we provide
experimental results to support our theoretical comparisons and illustrate when
our insights hold in finite-sample regimes and under various degrees of
misspecification.
