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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".