Order Optimal Bounds for One-Shot Federated Learning Over Non-Convex Loss Functions
Bibliographic record
Abstract
We consider the problem of federated learning in a one-shot setting in which there are$m$machines, each observing$n$sample functions from an unknown distribution on non-convex loss functions. Let$F:[-1,1]^{d}\to {\mathbb {R}} $be the expected loss function with respect to this unknown distribution. The goal is to find an estimate of the minimizer of$F$. Based on its observations, each machine generates a signal of bounded length$B$and sends it to a server. The server collects signals of all machines and outputs an estimate of the minimizer of$F$. We show that the expected loss of any algorithm is lower bounded by$\max \big (1/(\sqrt {n}(mB)^{1/d}), 1/\sqrt {mn}\big)$, up to a logarithmic factor. We then prove that this lower bound is order optimal in$m$and$n$by presenting a distributed learning algorithm, called Multi-Resolution Estimator for Non-Convex loss function (MRE-NC), whose expected loss matches the lower bound for large$mn$up to polylogarithmic factors.
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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 | 0.014 | 0.056 |
| Meta-epidemiology (narrow) | 0.006 | 0.002 |
| Meta-epidemiology (broad) | 0.007 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.006 | 0.012 |
| Open science | 0.008 | 0.007 |
| Research integrity | 0.007 | 0.010 |
| Insufficient payload (model declined to judge) | 0.013 | 0.004 |
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".