A unified modular analysis of online and stochastic optimization: adaptivity, optimism, non-convexity
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Bibliographic record
Abstract
We present a simple unified analysis of adaptive Mirror Descent (MD) and Follow- the-Regularized-Leader (FTRL) algorithms for online and stochastic optimization in (possibly infinite-dimensional) Hilbert spaces. The analysis is modular in the sense that it completely decouples the effect of possible assumptions on the loss functions (such as smoothness, strong convexity, and non-convexity) and on the optimization regularizers (such as strong convexity, non-smooth penalties in composite-objective learning, and non-monotone step-size sequences). We demonstrate the power of this decoupling by obtaining generalized algorithms and improved regret bounds for the so-called “adaptive optimistic online learning” set- ting. In addition, we simplify and extend a large body of previous work, including several various AdaGrad formulations, composite-objective and implicit-update algorithms. In all cases, the results follow as simple corollaries within few lines of algebra. Finally, the decomposition enables us to obtain preliminary global guarantees for limited classes of non-convex problems.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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