Networked Federated Multi-Task Learning. (arXiv:2105.12769v1 [cs.LG])

Many important application domains generate distributed collections of
heterogeneous local datasets. These local datasets are often related via an
intrinsic network structure that arises from domain-specific notions of
similarity between local datasets. Different notions of similarity are induced
by spatiotemporal proximity, statistical dependencies, or functional relations.
We use this network structure to adaptively pool similar local datasets into
nearly homogenous training sets for learning tailored models. Our main
conceptual contribution is to formulate networked federated learning using the
concept of generalized total variation (GTV) minimization as a regularizer.
This formulation is highly flexible and can be combined with almost any
parametric model including Lasso or deep neural networks. We unify and
considerably extend some well-known approaches to federated multi-task
learning. Our main algorithmic contribution is a novel federated learning
algorithm that is well suited for distributed computing environments such as
edge computing over wireless networks. This algorithm is robust against model
misspecification and numerical errors arising from limited computational
resources including processing time or wireless channel bandwidth. As our main
technical contribution, we offer precise conditions on the local models as well
on their network structure such that our algorithm learns nearly optimal local
models. Our analysis reveals an interesting interplay between the
(information-) geometry of local models and the (cluster-) geometry of their



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