Convergence analysis of a proximal stochastic gradient algorithm with adaptive sampling for non-convex and non-smooth composite optimization problems
Bibliographic record
Abstract
This paper examines the convergence and computational complexity of a proximal stochastic gradient algorithm that adaptively incorporates sampling techniques for solving large-scale, non-convex, and non-smooth problems, with a particular emphasis on problems that involve the combination of two non-convex functions.This an area that has been scarcely explored by current methods.By adjusting adaptively the sampling size (or mini-batch size) throughout the algorithm's iterations, this method aims to balance the trade-off between stochastic gradient noise and convergence stability.It maintains a convergence rate similar to that of the proximal gradient method.Moreover, when the objective function is a Kurdyka-Łojasiewicz (KL) function, we demonstrate the convergence rate of the expected function value on a case-by-case basis, achieving linear convergence under optimal conditions.Finally, some preliminary numerical results validate the effectiveness and robustness of the proposed method.
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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 | 0.005 | 0.010 |
| 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 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".