Stochastic Uncertain Systems Subject to Relative Entropy Constraints: Induced Norms and Monotonicity Properties of Minimax Games
Bibliographic record
Abstract
Entropy and relative entropy are fundamental concepts on which information theory is founded on, and in general, telecommunication systems design. On the other hand, dissipation inequalities, minimax strategies, and induced norms are the basic concepts on which robustness of uncertain control and estimation of systems are founded on. In this paper, the precise relation between these notions is investigated. In particular, it will be shown that the higher the dissipation the higher the entropy of the system, which has implications in computing the induced norm associated with robustness. These connections are obtained by considering stochastic optimal uncertain control systems, in which uncertainty is described by a relative entropy constraint between the nominal and uncertain measures, while the pay-off is a linear functional of the uncertain measure. This is a minimax game, in which the controller measure seeks to minimize the pay-off, while the disturbance measure aims at maximizing the pay-off. Salient properties of the minimax solution are derived, including a characterization of the optimal sensitivity reduction, computation of the induced norm, monotonicity properties of minimax solution, and relations between dissipation and relative entropy of the system. The theory is developed in an abstract setting and then applied to nonlinear partially observable continuous-time uncertain controlled systems, in which the nominal and uncertain systems are described by conditional distributions. In addition, existence of the optimal control policy among the class of policies known as wide-sense control laws is shown, and an explicit formulae for the worst case conditional measure is derived. The results are applied to linear-quadratic-Gaussian problems
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".