Zero-Delay Lossy Coding of Linear Vector Markov Sources with Applications to Networked Control
Bibliographic record
Abstract
In this thesis we study the optimal zero-delay coding (quantization) of $\\mathbb{R}^d$-valued linearly \ngenerated Markov sources under quadratic distortion. The structure and existence of \ndeterministic and stationary coding policies that are optimal for the infinite horizon average \ncost (distortion) problem is established. Prior results studying the optimality \nof zero-delay codes for Markov sources for infinite horizons either considered finite \nalphabet sources or, for the $\\mathbb{R}^d$-valued case, only showed the \nexistence of deterministic and non-stationary Markov coding policies or those \nwhich are randomized. In addition to existence results, for finite blocklength \n(horizon) $T$ the performance of an optimal coding policy is shown to approach \nthe infinite time horizon optimum at a rate $O(\\frac{1}{T})$. This gives an \nexplicit rate of convergence that quantifies the near-optimality of finite window (finite-memory) \ncodes among all optimal zero-delay codes. In addition, we present an important application of our result to closed loop networked control systems. We show that with predictive encoder the separation principle for the infinite horizon problem holds. Prior results only proved this for finite horizon average cost problem.
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How this classification was reachedexpand
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) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".