  Inverse optimization (IO) aims to determine optimization model parameters
from observed decisions. However, IO is not part of a data scientist's toolkit
in practice, especially as many general-purpose machine learning packages are
widely available as an alternative. When encountering IO, practitioners face
the question of when, or even whether, investing in developing IO methods is
worthwhile. Our paper provides a starting point toward answering these
questions, focusing on the problem of imputing the objective function of a
parametric convex optimization problem. We compare the predictive performance
of three standard supervised machine learning (ML) algorithms (random forest,
support vector regression and Gaussian process regression) to the performance
of the IO model of Keshavarz, Wang, and Boyd (2011). While the IO literature
focuses on the development of methods tailored to particular problem classes,
our goal is to evaluate general "out-of-the-box" approaches. Our experiments
demonstrate that determining whether to use an ML or IO approach requires
considering (i) the training set size, (ii) the dependence of the optimization
problem on external parameters, (iii) the level of confidence with regards to
the correctness of the optimization prior, and (iv) the number of critical
regions in the solution space.
