Networked Federated Learning

We develop the theory and algorithmic toolbox for networked federated learning in decentralized collections of local datasets with an intrinsic network structure. This network structure arises from domain-specific notions of similarity between local datasets. Different notions of similarity are induced by spatio-temporal proximity, statistical dependencies or functional relations. Our main conceptual contribution is to formulate networked federated learning using a generalized total variation minimization. This formulation unifies and considerably extends existing federated multi-task learning methods. It is highly flexible and can be combined with a broad range of parametric models including Lasso or deep neural networks. Our main algorithmic contribution is a novel networked federated learning algorithm which is well suited for distributed computing environments such as edge computing over wireless networks. This algorithm is robust against inexact computations arising from limited computational resources including processing time or bandwidth. For local models resulting in convex problems, we derive precise conditions on the local models and their network structure such that our algorithm learns nearly optimal local models. Our analysis reveals an interesting interplay between the convex geometry of local models and the (cluster-) geometry of their network structure

Local Graph Clustering with Network Lasso

We study the statistical and computational properties of a network Lasso method for local graph clustering. The clusters delivered by nLasso can be characterized elegantly via network flows between cluster boundaries and seed nodes. While spectral clustering methods are guided by a minimization of the graph Laplacian quadratic form, nLasso minimizes the total variation of cluster indicator signals. As demonstrated theoretically and numerically, nLasso methods can handle very sparse clusters (chain-like) which are difficult for spectral clustering. We also verify that a primal-dual method for non-smooth optimization allows to approximate nLasso solutions with optimal worst-case convergence rate.Peer reviewe