Comparing Inverse Optimization and Machine Learning Methods for Imputing a Convex Objective Function
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.033 | 0.123 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".