Bibliographic record
Abstract
We introduce a monotone and a non-monotone variant of the proximal gradient method in which the quadratic term is diagonal but may be indefinite, and is safeguarded by a trust region. Our method is a special case of the proximal quasi-Newton trust-region method of Aravkin et al. (SIAM J Optim 32(2):900–929, 2022). We provide closed-form solution of the step computation in certain cases where the nonsmooth term is separable and the trust region is defined in the infinity norm, so that no iterative subproblem solver is required. Our analysis expands upon that of (Aravkin et al. in SIAM J Optim 32(2):900–929, 2022) by generalizing the trust-region approach to problems with bound constraints. We provide an efficient open-source implementation of our method, named TRDH, in the Julia language in which Hessians approximations are given by diagonal quasi-Newton updates. TRDH evaluates one standard proximal operator and one indefinite proximal operator per iteration. We also analyze and implement a variant named iTRDH that performs a single indefinite proximal operator evaluation per iteration. We establish that iTRDH enjoys the same asymptotic worst-case iteration complexity as TRDH. We report numerical experience on unconstrained and bound-constrained problems, where TRDH and iTRDH are used both as standalone and subproblem solvers. Our results illustrate that, as standalone solvers, TRDH and iTRDH improve upon the quadratic regularization method R2 of (Aravkin et al. in SIAM J Optim 32(2):900–929, 2022) but also sometimes upon their quasi-Newton trust-region method, referred to here as TR-R2, in terms of smooth objective value and gradient evaluations. On challenging nonnegative matrix factorization, binary classification and data fitting problems, TRDH and iTRDH used as subproblem solvers inside TR improve upon TR-R2 for at least one choice of diagonal approximation and memory parameter.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".