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Inverse optimization (IO) aims to determine optimization model parametersfrom observed decisions. However, IO is not part of a data scientist's toolkitin practice, especially as many general-purpose machine learning packages arewidely available as an alternative. When encountering IO, practitioners facethe question of when, or even whether, investing in developing IO methods isworthwhile. Our paper provides a starting point toward answering thesequestions, focusing on the problem of imputing the objective function of aparametric convex optimization problem. We compare the predictive performanceof three standard supervised machine learning (ML) algorithms (random forest,support vector regression and Gaussian process regression) to the performanceof the IO model of Keshavarz, Wang, and Boyd (2011). While the IO literaturefocuses on the development of methods tailored to particular problem classes,our goal is to evaluate general "out-of-the-box" approaches. Our experimentsdemonstrate that determining whether to use an ML or IO approach requiresconsidering (i) the training set size, (ii) the dependence of the optimizationproblem on external parameters, (iii) the level of confidence with regards tothe correctness of the optimization prior, and (iv) the number of criticalregions in the solution space.

Comparing Inverse Optimization and Machine Learning Methods for Imputing a Convex Objective Function