Deep Structured Teams in Arbitrary-Size Linear Networks: Decentralized Estimation, Optimal Control and Separation Principle
Why this work is in the frame
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Bibliographic record
Abstract
In this article, we introduce decentralized Kalman filters for linear quadratic deep structured teams. The agents in deep structured teams are coupled in dynamics, costs and measurements through a set of linear regressions of the states and actions (also called deep states and deep actions). The information structure is decentralized, where every agent observes a noisy measurement of its local state and the global deep state. Since the number of agents is often very large in deep structured teams, any naive approach to finding an optimal Kalman filter suffers from the curse of dimensionality. Moreover, due to the decentralized nature of information structure, the resultant optimization problem is non-convex, in general, where non-linear strategies can outperform linear ones. However, we prove that the optimal strategy is linear in the local state estimate as well as the deep state estimate and can be efficiently computed by two scale-free Riccati equations and Kalman filters. We propose a bi-level orthogonal approach across both space and time levels based on a gauge transformation technique to achieve the above result. We also establish a separation principle between optimal control and optimal estimation. Furthermore, we show that as the number of agents goes to infinity, the Kalman gain associated with the deep state estimate converges to zero at a rate inversely proportional to the number of agents. This leads to a fully decentralized approximate strategy where every agent predicts the deep state by its conditional and unconditional expected value, also known as the certainty equivalence approximation and (weighted) mean-field approximation, respectively.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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 it