PAC-Bayes-Bernstein Inequality for Martingales and its Application to\n Multiarmed Bandits
Bibliographic record
Abstract
We develop a new tool for data-dependent analysis of the\nexploration-exploitation trade-off in learning under limited feedback. Our tool\nis based on two main ingredients. The first ingredient is a new concentration\ninequality that makes it possible to control the concentration of weighted\naverages of multiple (possibly uncountably many) simultaneously evolving and\ninterdependent martingales. The second ingredient is an application of this\ninequality to the exploration-exploitation trade-off via importance weighted\nsampling. We apply the new tool to the stochastic multiarmed bandit problem,\nhowever, the main importance of this paper is the development and understanding\nof the new tool rather than improvement of existing algorithms for stochastic\nmultiarmed bandits. In the follow-up work we demonstrate that the new tool can\nimprove over state-of-the-art in structurally richer problems, such as\nstochastic multiarmed bandits with side information (Seldin et al., 2011a).\n
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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 | 0.011 | 0.044 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".