The paper derives Wasserstein-based generalization bounds for hierarchical federated learning via a tree-structured supersample construction that recover CMI bounds for bounded losses and match the asymptotic rate in the Gaussian location model.
Their supersample has one extra index because they average the information metric over the whole ghost subtree, not only the intermediate node
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A Hierarchical Sampling Framework for bounding the Generalization Error of Federated Learning
The paper derives Wasserstein-based generalization bounds for hierarchical federated learning via a tree-structured supersample construction that recover CMI bounds for bounded losses and match the asymptotic rate in the Gaussian location model.