  Non-Independent and Identically Distributed (non- IID) data distribution
among clients is considered as the key factor that degrades the performance of
federated learning (FL). Several approaches to handle non-IID data such as
personalized FL and federated multi-task learning (FMTL) are of great interest
to research communities. In this work, first, we formulate the FMTL problem
using Laplacian regularization to explicitly leverage the relationships among
the models of clients for multi-task learning. Then, we introduce a new view of
the FMTL problem, which in the first time shows that the formulated FMTL
problem can be used for conventional FL and personalized FL. We also propose
two algorithms FedU and dFedU to solve the formulated FMTL problem in
communication-centralized and decentralized schemes, respectively.
Theoretically, we prove that the convergence rates of both algorithms achieve
linear speedup for strongly convex and sublinear speedup of order 1/2 for
nonconvex objectives. Experimentally, we show that our algorithms outperform
the algorithm FedAvg, FedProx, SCAFFOLD, and AFL in FL settings, MOCHA in FMTL
settings, as well as pFedMe and Per-FedAvg in personalized FL settings.
