On the optimal thresholds in remote state estimation with communication costs
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Bibliographic record
Abstract
In this paper, we consider a remote sensing system that consists of a sensor and an estimator. A sensor observes a first order Markov source and must communicate it to a remote estimator. Communication is noiseless but expensive. At each time, based on the history of its observations and decisions, the sensor chooses whether to transmit or not. If the sensor does not transmit, then the estimator must estimate the Markov process using its past observations. It was shown by Lipsa and Martins, 2011 and by Nayyar et al, 2013 that the optimal strategy has the following structure. The optimal estimation strategy is Kalman-like and the optimal communication strategy is to communicate when the estimation error is greater than a threshold. We derive closed form expressions for infinite horizon discounted cost version of the problem. Our solution approach is inspired by the idea of calibration used in multi-armed bandits. We identify the value of the communication cost for which one is indifferent between two consecutive threshold based strategies. Using these values, we characterize the optimal thresholds as a function of the communication cost. Lastly, we present an example of birth-death Markov chain to illustrate our results.
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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 | 0.000 |
| 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) | 0.000 | 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