Monotonicity of Constrained Optimal Transmission Policies in Correlated Fading Channels With ARQ
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Bibliographic record
Abstract
We consider transmission scheduling using an ARQ protocol with retransmissions given channel state information (CSI) and a correlated fading channel. The problem is formulated as a countable state, infinite horizon, average cost Markov decision process (MDP) with an average delay constraint. Our main result is to give sufficient conditions on the channel memory, and transmission cost so that the optimal transmission scheduling policy is a monotonically increasing function of the buffer occupancy. In proving this result, we first prove positive recurrence (stability) of the buffer. The monotone structure proof consists of two steps. First, the constrained MDP (CMDP) is transformed into an unconstrained MDP using a Lagrangian dynamic programming formulation. It is proved that the unconstrained optimal policy is pure and monotonically increasing in the buffer occupancy. It is then shown that the constrained optimal policy is a randomized mixture of two pure transmission policies that are monotone in the buffer state. Finally, the monotone structure of the optimal transmission policy is exploited to derive a monotone-policy <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> -learning algorithm and a stochastic approximation based monotone policy search algorithm for estimating the optimal policy in real time.
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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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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