Continuous-time distributed convex optimization on time-varying directed networks
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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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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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