Efficient Gradient-Enhanced Bayesian Optimizer with Comparisons to Conjugate-Gradient and Quasi-Newton Optimizers for Unconstrained Local Optimization
Why this work is in the frame
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Bibliographic record
Abstract
The probabilistic surrogates used by Bayesian optimizers make them popular methods when function evaluations are noisy or expensive to evaluate. While Bayesian optimizers are traditionally used for global optimization, their benefits are also valuable for local optimization. In this paper, a framework for gradient-enhanced unconstrained local Bayesian optimization is presented. It involves selecting a subset of the evaluation points to construct the surrogate and using a probabilistic trust region for the minimization of the acquisition function. The Bayesian optimizer is compared to conjugate-gradient and quasi-Newton optimizers from MATLAB and SciPy for unimodal problems with 2 to 40 dimensions. The Bayesian optimizer converges the optimality as deeply as the optimizers used for comparison and often does so using significantly fewer function evaluations. For the minimization of the 40-dimensional Rosenbrock function for example, the Bayesian optimizer requires half as many function evaluations as the MATLAB and SciPy optimizers to reduce the optimality by 10 orders of magnitude. For test cases with noisy gradients, the probabilistic surrogate of the Bayesian optimizer enables it to converge the optimality several additional orders of magnitude relative to the conjugate-gradient and quasi-Newton optimizers. The final test case involves the chaotic Lorenz 63 model and inaccurate gradients. For this problem, the Bayesian optimizer achieves a lower final objective evaluation than the SciPy quasi-Newton optimizer for all initial starting solutions. The results demonstrate that a Bayesian optimizer can be competitive with quasi-Newton and conjugate-gradient optimizers when accurate gradients are available, and significantly outperforms them when the gradients are innacurate.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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