Continuous-time distributed convex optimization on time-varying directed networks
Bibliographic record
Abstract
We introduce a general class of continuous-time distributed control systems, where the control input to the dynamics of each agent relies on an observer that estimates the average state. The dynamics of these observers are nonlinear, but the agents only need to have access to local information to implement them. We show that under a general condition on the structure of the underlying time-varying directed graphs, the difference of the agents' estimates and the true average is upper bounded. Using this result, we show that when we have a class P* weakly exponentially ergodic flow and the agent's objective functions are differentiable with bounded gradients, any trajectory of the proposed continuous-time dynamics is globally asymptotically convergent to a minimizer. Finally, we demonstrate that the class P* weakly exponentially ergodic flow property can be achieved by assuming that the sequence of Laplacians are measurable, cut-balanced, and has a minimum instantaneous flow. As a by-product, we show that the proposed continuous-time dynamics for distributed convex optimization is convergent on any sequence of time-varying strongly connected directed graph.
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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 | 0.001 | 0.002 |
| 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 | 0.001 |
| 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".