Bibliographic record
Abstract
We propose an alternating subgradient method with non-constant step sizes for solving convex-concave saddle-point problems associated with general convex-concave functions. We assume that the sequence of our step sizes is not summable but square summable. Then under the popular assumption of uniformly bounded subgradients, we prove that a sequence of convex combinations of function values over our iterates converges to the value of the function at a saddle-point. Additionally, based on our result regarding the boundedness of the sequence of our iterates, we show that a sequence of the function evaluated at convex combinations of our iterates also converges to the value of the function over a saddle-point. We implement our algorithms in examples of a linear program in inequality form, a least-squares problem with $\ell_{1}$ regularization, a matrix game, and a robust Markowitz portfolio construction problem. To accelerate convergence, we reorder the sequence of step sizes in descending order, which turned out to work very-well in our examples. Our convergence results are confirmed by our numerical experiments. Moreover, we also numerically compare our iterate scheme with iterates schemes associated with constant step sizes. Our numerical results support our choice of step sizes. Additionally, we observe the convergence of the sequence of function values over our iterates in multiple experiments, which currently lacks theoretical support.
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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 | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".