A Modified Distributed Gradient Dynamics for Multiagent Optimization on Directed Networks
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Bibliographic record
Abstract
This paper considers the distributed convex optimization problem over directed multi-agent networks. We introduce a continuous-time coordination algorithm to solve unconstrained optimization problems with additive structure. The proposed algorithm can be interpreted as a modified version of the distributed subgradient method, enhanced with an augmented scalar state variable. Each agent is assumed to know its out-degree. Unlike existing methods that rely on a perturbed version of the push-sum algorithm, the proposed algorithm does not require any specific initialization. As a result, it is capable of handling strongly connected networks with sporadically varying sizes. We show that the proposed network flow is guaranteed to converge to the global minimizer of a sum of convex functions, provided that the local objective functions are strongly convex and have Lipschitz-continuous gradients. Additionally, by considering a class of admissible time-varying gains/step-sizes, our analysis substantiates an explicit sublinear rate of convergence for the proposed algorithm.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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