A vector almost-supermartingale convergence theorem and its applications
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Bibliographic record
Abstract
The almost-supermartingale convergence theorem of Robbins and Siegmund (1971) is a fundamental tool for establishing the convergence of various stochastic iterative algorithms including system identification, adaptive control, and reinforcement learning. The theorem is stated for non-negative scalar valued stochastic processes. In this paper, we generalize the theorem to non-negative vector valued stochastic processes and provide two set of sufficient conditions for such processes to converge almost surely. We present several applications of vector almost-supermartingale convergence theorem, including convergence of autoregressive supermartingales, delayed supermartingales, and stochastic approximation with delayed updates.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it