An Inexact Modified Quasi-Newton Method for Nonsmooth Regularized Optimization
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Bibliographic record
Abstract
We introduce iR2N, a modified proximal quasi-Newton method for minimizing the sum of a smooth function $f$ and a lower semi-continuous prox-bounded function $h$, allowing inexact evaluations of $f$, its gradient, and the associated proximal operators. Both $f$ and $h$ may be nonconvex. iR2N is particularly suited to settings where proximal operators are computed via iterative procedures that can be stopped early, or where the accuracy of $f$ and $\nabla f$ can be controlled, leading to significant computational savings. At each iteration, the method approximately minimizes the sum of a quadratic model of $f$, a model of $h$, and an adaptive quadratic regularization term ensuring global convergence. Under standard accuracy assumptions, we prove global convergence in the sense that a first-order stationarity measure converges to zero, with worst-case evaluation complexity $O(ε^{-2})$. Numerical experiments with $\ell_p$ norms, $\ell_p$ total variation, and the indicator of the nonconvex pseudo $p$-norm ball illustrate the effectiveness and flexibility of the approach, and show how controlled inexactness can substantially reduce computational effort.
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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 | 0.001 | 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 | 0.001 |
| Open science | 0.001 | 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