A Framework for Nonlinearly‐Constrained Gradient‐Enhanced Local Bayesian Optimization With Comparisons to Quasi‐Newton Optimizers
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Bibliographic record
Abstract
ABSTRACT Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to leverage gradients, and their efficient use of noisy data. Bayesian optimizers have commonly been applied to global unconstrained problems, with limited development for many other classes of problems. In this article, two alternative methods are developed that enable rapid and deep convergence of nonlinearly‐constrained local optimization problems using a Bayesian optimizer. The first method uses an exact augmented Lagrangian and the second augments the minimization of the acquisition function to contain additional constraints. Both of these methods can be applied to nonlinear equality constraints, unlike most previous methods developed for constrained Bayesian optimizers. The new methods are applied with a gradient‐enhanced Bayesian optimizer and enable deeper convergence for three nonlinearly‐constrained unimodal optimization problems than previously developed methods for constrained Bayesian optimization. In addition, both new methods enable the Bayesian optimizer to reach a desired tolerance with fewer function evaluations than popular quasi‐Newton optimizers from SciPy and MATLAB for unimodal problems with 2 to 30 variables. The Bayesian optimizer had similar results using both methods. It is recommended that users first try using the second method, which adds constraints to the acquisition function minimization, since its parameters are more intuitive to tune for new problems.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it