Relaxing the i.i.d. assumption: Adaptively minimax optimal regret via root-entropic regularization
Bibliographic record
Abstract
We consider prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. This semi-adversarial setting includes (at the extremes) the classical i.i.d. setting, when the unknown constraint set is restricted to be a singleton, and the unconstrained adversarial setting, when the constraint set is the set of all distributions. The Hedge algorithm—long known to be minimax (rate) optimal in the adversarial regime—was recently shown to be simultaneously minimax optimal for i.i.d. data. In this work, we propose to relax the i.i.d. assumption by seeking adaptivity at all levels of a natural ordering on constraint sets. We provide matching upper and lower bounds on the minimax regret at all levels, show that Hedge with deterministic learning rates is suboptimal outside of the extremes and prove that one can adaptively obtain minimax regret at all levels. We achieve this optimal adaptivity using the follow-the-regularized-leader (FTRL) framework, with a novel adaptive regularization scheme that implicitly scales as the square root of the entropy of the current predictive distribution, rather than the entropy of the initial predictive distribution. Finally, we provide novel technical tools to study the statistical performance of FTRL along the semi-adversarial spectrum.
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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 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| 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 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".