On Convergence Rate of Distributed Stochastic Gradient Algorithm for Convex Optimization with Inequality Constraints
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Bibliographic record
Abstract
In this paper, we consider an optimization problem, where multiple agents cooperate to minimize the sum of their local individual objective functions subject to a global inequality constraint. We propose a class of distributed stochastic gradient algorithms that solve the problem using only local computation and communication. The implementation of the algorithms removes the need for performing the intermediate projections. For strongly convex optimization, we employ a smoothed constraint incorporation technique to show that the algorithm converges at an expected rate of $\mathcal{O}(\ln T / T)$ (where $T$ is the number of iterations) with bounded gradients. For non-strongly convex optimization, we use a reduction technique to establish an $\mathcal{O}(1/\sqrt{T})$ convergence rate in expectation. Finally, a numerical example is provided to show the convergence of the proposed algorithms.
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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 | 0.000 |
| 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 it