A Conclusive Analysis of the Finite-Time Behavior of the Discretized Pursuit Learning Automaton
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Bibliographic record
Abstract
This paper deals with the finite-time analysis (FTA) of learning automata (LA), which is a topic for which very little work has been reported in the literature. This is as opposed to the asymptotic steady-state analysis for which there are, probably, scores of papers. As clarified later, unarguably, the FTA of Markov chains, in general, and of LA, in particular, is far more complex than the asymptotic steady-state analysis. Such an FTA provides rigid bounds for the time required for the LA to attain to a given convergence accuracy. We concentrate on the FTA of the Discretized Pursuit Automaton (DPA), which is probably one of the fastest and most accurate reported LA. Although such an analysis was carried out many years ago, we record that the previous work is flawed. More specifically, in all brevity, the flaw lies in the wrongly "derived" monotonic behavior of the LA after a certain number of iterations. Rather, we claim that the property should be invoked is the submartingale property. This renders the proof to be much more involved and deep. In this paper, we rectify the flaw and reestablish the FTA based on such a submartingale phenomenon. More importantly, from the derived analysis, we are able to discover and clarify, for the first time, the underlying dilemma between the DPA's exploitation and exploration properties. We also nontrivially confirm the existence of the optimal learning rate, which yields a better comprehension of the DPA itself.
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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 | 0.000 | 0.000 |
| 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 | 0.001 |
| 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