Large-Population Risk Sensitive Linear-Quadratic Optimal Control: Decentralized Feedback
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Bibliographic record
Abstract
This paper studies a class of risk sensitive linear-quadratic social optimal control problems. We first overview the direct approach which solves the N-agent problem and constructs the limiting decentralized individual control laws by letting N tend to infinity. However, unlike the case of mean field games, the resulting decentralized control law leads to a persistent cost gap with respect to the centralized optimal control law, and can even be outperformed by other decentralized control laws.To derive the optimal decentralized control law, we develop a person-by-person (PbP) optimality approach. We first decompose the system states into observable and unobservable components, and then formulate the problem as a partially observed optimal control problem for a single agent. Although the cost faced by the agent increases with N, this method gives a meaningful limit of the solution. We further establish asymptotic optimality of the limit solution-based decentralized control law within the class of decentralized control laws. Numerical solutions demonstrate that the PbP optimality-based decentralized control law achieves notable performance gain with respect to the previous limit decentralized control law via the direct approach.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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