A Note on the Separation of Optimal Quantization and Control Policies in Networked Control
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Bibliographic record
Abstract
For controlled $\mathbb{R}^n$-valued linear systems driven by Gaussian noise under quadratic cost criteria, we revisit the problem of the structure of optimal quantization and control policies. In a recent paper [IEEE Trans. Automat. Control, 59 (2014), pp. 1612--1617] by the author, for fully observed and partially observed systems, the global optimality of predictive encoders was established under quadratic cost criteria. Furthermore, optimal control policies were shown to be linear in the conditional estimate of the state, and a form of separation of estimation and control was established. The present note does not introduce any new results or new conditions but clarifies that the results have been mischaracterized in the recent paper [M. Rabi, C. Ramesh, and K. H. Johansson, SIAM J. Control Optim., 54 (2016), pp. 662--689]. Since perhaps the arguments in [IEEE Trans. Automat. Control, 59 (2014), pp. 1612--1617] were concise and this led to the confusion, its key result is presented here with a more detailed proof.
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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 | 0.001 | 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