Online-to-Confidence-Set Conversions and Application to Sparse Stochastic Bandits
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Bibliographic record
Abstract
We introduce a novel technique, which we call online-to-confidence-set conversion. The technique allows us to construct highprobability confidence sets for linear prediction with correlated inputs given the predictions of any algorithm (e.g., online LASSO, exponentiated gradient algorithm, online least-squares, p-norm algorithm) targeting online learning with linear predictors and the quadratic loss. By construction, the size of the confidence set is directly governed by the regret of the online learning algorithm. Constructing tight confidence sets is interesting on its own, but the new technique is given extra weight by the fact having access tight confidence sets underlies a number of important problems. The advantage of our construction here is that progress in constructing better algorithms for online prediction problems directly translates into tighter confidence sets. In this paper, this is demonstrated in the case of linear stochastic bandits. In particular, we introduce the sparse variant of linear stochastic bandits and show that a recent online algorithm together with our online-to-confidence-set conversion allows one to derive algorithms that can exploit if the reward is a function of a sparse linear combination of the components of the chosen action.
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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 | 0.003 |
| 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 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.005 |
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