Pure entropic regularization for metrical task systems
Why this work is in the frame
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Bibliographic record
Abstract
<p>We show that on every <i>n</i>-point HST metric, there is a randomized online algorithm for metrical task systems (MTS) that is 1-competitive for service costs and <i>O</i>(log <i>n</i>)-competitive for movement costs. In general, these refined guarantees are optimal up to the implicit constant. While an <i>O</i>(log <i>n</i>)-competitive algorithm for MTS on HST metrics was developed by Bubeck et al. (SODA'19), that approach could only establish an <i>O</i>((log <i>n</i>)<sup>2</sup>)-competitive ratio when the service costs are required to be <i>O</i>(1)-competitive. Our algorithm can be viewed as an instantiation of online mirror descent with the regularizer derived from a multiscale conditional entropy.</p><br>\n\n<p>In fact, our algorithm satisfies a set of even more refined guarantees; we are able to exploit this property to combine it with known random embedding theorems and obtain, for <i>any</i> <i>n</i>-point metric space, a randomized algorithm that is 1-competitive for service costs and <i>O</i>((log <i>n</i>)<sup>2</sup>)-competitive for movement costs.</p>
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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 | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.001 |
| 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