Asymmetrically Decentralized Federated Learning

To address the communication burden and privacy concerns associated with the centralized server in Federated Learning (FL), Decentralized Federated Learning (DFL) has emerged, which discards the server with a peer-to-peer (P2P) communication framework. However, most existing DFL algorithms are based on symmetric topologies, such as ring and grid topologies, which can easily lead to deadlocks and are susceptible to the impact of network link quality in practice. To address these issues, this paper proposes the DFedSGPSM algorithm, which is based on asymmetric topologies and utilizes the Push-Sum protocol to effectively solve consensus optimization problems. To further improve algorithm performance and alleviate local heterogeneous overfitting in Federated Learning (FL), our algorithm combines the Sharpness Aware Minimization (SAM) optimizer and local momentum. The SAM optimizer employs gradient perturbations to generate locally flat models and searches for models with uniformly low loss values, mitigating local heterogeneous overfitting. The local momentum accelerates the optimization process of the SAM optimizer. Theoretical analysis proves that DFedSGPSM achieves a convergence rate of $\mathcal{O}(\frac{1}{\sqrt{T}})$ in a non-convex smooth setting under mild assumptions. This analysis also reveals that better topological connectivity achieves tighter upper bounds. Empirically, extensive experiments are conducted on the MNIST, CIFAR10, and CIFAR100 datasets, demonstrating the superior performance of our algorithm compared to state-of-the-art optimizers.

DFedADMM: Dual Constraints Controlled Model Inconsistency for Decentralized Federated Learning

To address the communication burden issues associated with federated learning (FL), decentralized federated learning (DFL) discards the central server and establishes a decentralized communication network, where each client communicates only with neighboring clients. However, existing DFL methods still suffer from two major challenges: local inconsistency and local heterogeneous overfitting, which have not been fundamentally addressed by existing DFL methods. To tackle these issues, we propose novel DFL algorithms, DFedADMM and its enhanced version DFedADMM-SAM, to enhance the performance of DFL. The DFedADMM algorithm employs primal-dual optimization (ADMM) by utilizing dual variables to control the model inconsistency raised from the decentralized heterogeneous data distributions. The DFedADMM-SAM algorithm further improves on DFedADMM by employing a Sharpness-Aware Minimization (SAM) optimizer, which uses gradient perturbations to generate locally flat models and searches for models with uniformly low loss values to mitigate local heterogeneous overfitting. Theoretically, we derive convergence rates of $\small \mathcal{O}\Big(\frac{1}{\sqrt{KT}}+\frac{1}{KT(1-\psi)^2}\Big)$ and $\small \mathcal{O}\Big(\frac{1}{\sqrt{KT}}+\frac{1}{KT(1-\psi)^2}+ \frac{1}{T^{3/2}K^{1/2}}\Big)$ in the non-convex setting for DFedADMM and DFedADMM-SAM, respectively, where $1 - \psi$ represents the spectral gap of the gossip matrix. Empirically, extensive experiments on MNIST, CIFAR10 and CIFAR100 datesets demonstrate that our algorithms exhibit superior performance in terms of both generalization and convergence speed compared to existing state-of-the-art (SOTA) optimizers in DFL.