Convergence Rates of Epsilon-Greedy Global Optimization Under Radial Basis Function Interpolation
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Bibliographic record
Abstract
We study a global optimization problem where the objective function can be observed exactly at individual design points with no derivative information. We suppose that the design points are determined sequentially using an epsilon-greedy algorithm, that is, by sampling uniformly on the design space with a certain probability and otherwise sampling in a local neighborhood of the current estimate of the best solution. We study the rate at which the estimate converges to the global optimum and derive two types of bounds: an asymptotic pathwise rate and a concentration inequality measuring the likelihood that the asymptotic rate has not yet gone into effect. The order of the rate becomes faster when the width of the local search neighborhood is made to shrink over time at a suitably chosen speed.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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