An adaptive self-regular proximity-based large-update IPM for LO
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Bibliographic record
Abstract
Primal–dual interior-point methods (IPMs) have shown their power in solving large classes of optimization problems. However, there is still a discrepancy between the practical behavior of these algorithms and their theoretical worst-case complexity results with respect to the update strategies of the dua-lity gap parameter in the algorithm. Recently, this discrepancy was significantly reduced by Peng, J., Roos, C. and Terlaky, T., 2002, Self-Regularity: A New Paradigm for Primal–Dual Interior-Point Algorithms (Princeton, NJ: Princeton University Press) who introduced a new family of self-regular (SR)-proximity functions based IPMs. In this paper, based on a class of SR proximities, we propose an adaptive single-step large-update SR-IPM that is very close to what is used in the McIPM software package. At each step, our algorithm always chooses a large-update of the target value adaptively depending on the position of the current iterate. This adaptive choice of the target value is different from the one what is presented in Peng, J., Roos, C. and Terlaky, T., 2002, Self-Regularity: A New Paradigm for Primal–Dual Interior-Point Algorithms (Princeton, NJ: Princeton University Press), where the target μ value is reduced by a fix factor when the iterate is sufficiently well centered. An 𝒪(qn ( q +1)/2 q log(n/ϵ)) worst-case iteration bound of the algorithm is established, where q is the barrier degree of the SR-proximity. For q = log n, our algorithm achieves the so far best complexity for large-update IPMs.
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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 | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.001 | 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