Social optima in linear quadratic graphon field control: Analysis via infinite dimensional approach
Bibliographic record
Abstract
This paper is concerned with a class of linear quadratic graphon field social control problems where the noises of individual agents are correlated.Compared with the well-studied mean field system, the graphon field system consists of a large number of agents coupled weakly via a weighted undirected graph where each node represents an individual agent.Another notable feature of this paper is that the dynamics of states of agents are driven by Brownian motions with a correlation matrix.The infinite dimensional approach is adopted to design the centralized and decentralized controls for our large population system.By graphon theory, we prove that the linear quadratic (LQ) social control problem under the centralized information pattern is equivalent to an LQ optimal control problem concerned with a stochastic evolution equation, and the feedback-type optimal centralized control is obtained.Then, by designing an auxiliary infinite dimensional optimal control problem through agent number N → ∞, a set of decentralized strategies are constructed, which are further demonstrated to be asymptotically social optimal.
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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 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| 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".