A derivative-free comirror algorithm for convex optimization
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Bibliographic record
Abstract
We consider the minimization of a nonsmooth convex function over a compact convex set subject to a nonsmooth convex constraint. We work in the setting of derivative-free optimization (DFO), assuming that the objective and constraint functions are available through a black-box that provides function values for lower- representation of the functions. Our approach is based on a DFO adaptation of the ε-comirror algorithm [Beck et al. The CoMirror algorithm for solving nonsmooth constrained convex problems, Oper. Res. Lett. 38(6) (2010), pp. 493–498]. Algorithmic convergence hinges on the ability to accurately approximate subgradients of lower- functions, which we prove is possible through linear interpolation. We show that, if the sampling radii for linear interpolation are properly selected, then the new algorithm has the same convergence rate as the original gradient-based algorithm. This provides a novel global rate-of-convergence result for nonsmooth convex DFO with nonsmooth convex constraints. We conclude with numerical testing that demonstrates the practical feasibility of the algorithm and some directions for further research.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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 |
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