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Connecting Federated ADMM to Bayes
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Working notes (drafts and update logs) for a federated learning method that sends function-space information over memory/unlabelled points and combines ideas from K-priors, DNN2GP, and PVI/EP; no experiments are finalized and the text is not a finished paper.
Problem
Federated learning where clients should send information about their own data (rather than weights) so a global model reaches the ideal centralised solution; the notes explore how to do this without sending raw data.
Approach
Derives a federated algorithm from Gaussian/Laplace approximations of posteriors, where each client sends weight-space and function-space (memory-point) information, and clients correct the global parameters using their own true labels; the notes claim the ideal solution is a stationary point and that the method works on 2D toy GLMs.
Key results
- On a 2D toy example, after two communication rounds the proposed algorithm reaches 99% train accuracy (NLL 40) versus 98% (NLL 60) for a baseline that trains on all data then sends predictions over unlabelled points.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed method for 2 communication rounds instead of the baseline with unlabelled data | Federated learning on Toy-Gaussians · Toy-Gaussians train | accuracy: 98% -> 99% | Helped |
| Use the proposed method for 2 communication rounds instead of the baseline with unlabelled data | Federated learning on Toy-Gaussians · Toy-Gaussians train | nll: 60 -> 40 | Helped |
| Send predictions over all clients' unlabelled points instead of only each client's own points (ablation) | Proposed federated method · Toy-Gaussians | performance | No clear effect |
Surprising findings
- The algorithm performed better than the alternative baseline on the toy example, which the author could not explain theoretically.
Limitations
- Theoretical convergence to the ideal solution is not proven; only stationarity of the ideal solution is sketched.
- Experiments are limited to 2D toy classification with GLMs; MLP results are described as brittle.
- Choice of memory points and weighting is unresolved.
Experimental setup
Datasets: Toy-Gaussians (2D binary classification, synthetic)
Metrics: train accuracy negative log-likelihood
Baselines: FedAvg Improved K-priors
Builds on: K-priors DNN2GP PVI FROMP
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