Large-Population Risk Sensitive Linear-Quadratic Optimal Control: Decentralized Feedback
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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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".