A formal proof of the e-optimality of discretized pursuit algorithms
Bibliographic record
Abstract
Learning Automata (LA) can be reckoned to be the founding algorithms on which the field of Reinforcement Learning has been built.Among the families of LA, Estimator Algorithms (EAs) are certainly the fastest, and of these, the family of discretized algorithms are proven to converge even faster than their continuous counterparts.However, it has recently been reported that the previous proofs for ε-optimality for all the reported algorithms for the past three decades have been flawed 1 .We applaud the researchers who discovered this flaw, and who further proceeded to rectify the proof for the Continuous Pursuit Algorithm (CPA).The latter proof examines the monotonicity property of the probability of selecting the optimal action, and requires the learning parameter to be continuously changing.In this paper, we provide a new method to prove the ε-optimality of the Discretized Pursuit Algorithm (DPA) which does not require this constraint, by virtue of the fact that the DPA has, in and of itself, absorbing barriers to which the LA can jump in a discretized manner.Unlike the proof given [3] for an absorbing version of the CPA, which utilizes the single-action Hoeffding's inequality, the current proof invokes, what we shall refer to, as the "multi-action" version of the Hoeffding's inequality.We believe that our proof is both unique and pioneering.It can also form the basis for formally showing the ε-optimality of the other EAs that possess absorbing states.
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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 | 0.033 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.002 | 0.007 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.014 | 0.002 |
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".