# A New Look and Convergence Rate of Federated Multi-Task Learning with Laplacian Regularization Source: [A New Look and Convergence Rate of Federated Multi-Task Learning with Laplacian Regularization]() Collection index: [llms.txt]() Data updated: 2025-10-26T00:39:21.820Z Authors: Canh T. Dinh, Tung T. Vu, Nguyen H. Tran, Minh N. Dao, Hongyu Zhang Published: 2021-02-14T13:19:43.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on CIFAR-100 Noisy 100 clients (test)](): Image Classification; CIFAR-100 Noisy 100 clients (test); Relative Accuracy Decrease (%): -2.8. - [Image Classification on CINIC-10 (test)](): Image Classification; CINIC-10 (test); Accuracy: 59.3. - [Image Classification on CIFAR-10 (test)](): Image Classification; CIFAR-10 (test); Accuracy: 80.6. - [Image Classification on CIFAR-100 (test)](): Image Classification; CIFAR-100 (test); Accuracy: 41.1. ## Original sources and implementation [Original paper]() [PDF]()