Decentralized Federated Learning has emerged as an alternative to centralized architectures due to its faster training, privacy preservation, and reduced communication overhead. In decentralized communication, the server aggregation phase in Centralized Federated Learning shifts to the client side, which means that clients connect with each other in a peer-to-peer manner. However, compared to the centralized mode, data heterogeneity in Decentralized Federated Learning will cause larger variances between aggregated models, which leads to slow convergence in training and poor generalization performance in tests. To address these issues, we introduce Catalyst Acceleration and propose an acceleration Decentralized Federated Learning algorithm called DFedCata. It consists of two main components: the Moreau envelope function, which primarily addresses parameter inconsistencies among clients caused by data heterogeneity, and Nesterov's extrapolation step, which accelerates the aggregation phase. Theoretically, we prove the optimization error bound and generalization error bound of the algorithm, providing a further understanding of the nature of the algorithm and the theoretical perspectives on the hyperparameter choice. Empirically, we demonstrate the advantages of the proposed algorithm in both convergence speed, computational cost, and generalization performance on CIFAR10/100 and Tiny-ImageNet with various non-iid data distributions. Moreover, extensive experiments are conducted to validate the theoretical properties of DFedCata, showing strong consistency between theory and empirical observations.

Despite great achievements in algorithm design for Personalized Federated Learning (PFL), research on the theoretical analysis of generalization is still in its early stages. Some theoretical results have investigated the generalization performance of personalized models under the problem setting and hypothesis in convex conditions, which can not reflect the real iteration performance during non-convex training. To further understand the real performance from a generalization perspective, we propose the first algorithm-dependent generalization analysis with uniform stability for the typical PFL method, Partial Model Personalization, on smooth and non-convex objectives. Specifically, we decompose the generalization errors into aggregation errors and fine-tuning errors, then creatively establish a generalization analysis framework corresponding to the gradient estimation process of the personalized training. This framework builds up the bridge among PFL, FL and Pure Local Training for personalized aims in heterogeneous scenarios, which clearly demonstrates the effectiveness of PFL from the generalization perspective. Moreover, we demonstrate the impact of trivial factors like learning steps, stepsizes and communication topologies and obtain the excess risk analysis with optimization errors for PFL. Promising experiments on CIFAR datasets also corroborate our theoretical insights. Our code can be seen in https://github.com/YingqiLiu1999/Understanding-the-Stability-based-Generalization-of-Personalized-Federated-Learning.

Decentralized training removes the centralized server, making it a communication-efficient approach that can significantly improve training efficiency, but it often suffers from degraded performance compared to centralized training. Multi-Gossip Steps (MGS) serve as a simple yet effective bridge between decentralized and centralized training, significantly reducing experiment performance gaps. However, the theoretical reasons for its effectiveness and whether this gap can be fully eliminated by MGS remain open questions. In this paper, we derive upper bounds on the generalization error and excess error of MGS using stability analysis, systematically answering these two key questions. 1). Optimization Error Reduction: MGS reduces the optimization error bound at an exponential rate, thereby exponentially tightening the generalization error bound and enabling convergence to better solutions. 2). Gap to Centralization: Even as MGS approaches infinity, a non-negligible gap in generalization error remains compared to centralized mini-batch SGD ($\mathcal{O}(T^{\frac{c\beta}{c\beta +1}}/{n m})$ in centralized and $\mathcal{O}(T^{\frac{2c\beta}{2c\beta +2}}/{n m^{\frac{1}{2c\beta +2}}})$ in decentralized). Furthermore, we provide the first unified analysis of how factors like learning rate, data heterogeneity, node count, per-node sample size, and communication topology impact the generalization of MGS under non-convex settings without the bounded gradients assumption, filling a critical theoretical gap in decentralized training. Finally, promising experiments on CIFAR datasets support our theoretical findings.

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 existing DFL methods have not fundamentally addressed. To tackle these issues, we propose novel DFL algorithms, DFedADMM and its enhanced version DFedADMM-SAM, to improve the performance for 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 $\mathcal {O}(\frac{1}{\sqrt{KT}}+\frac{1}{KT(1-\psi )^{2}})$O(1KT+1KT(1-ψ)2) and $ \mathcal {O}(\frac{1}{\sqrt{KT}}+\frac{1}{KT(1-\psi )^{2}}+ \frac{1}{T^{3/2}K^{1/2}})$O(1KT+1KT(1-ψ)2+1T3/2K1/2) in the non-convex setting for DFedADMM and DFedADMM-SAM, respectively, where $1 - \psi$1-ψ represents the spectral gap of the gossip matrix. Empirically, extensive experiments on MNIST, CIFAR10, and CIFAR100 datasets demonstrate that our algorithms exhibit superior performance in terms of generalization, convergence speed, and communication overhead compared to existing state-of-the-art (SOTA) optimizers in DFL.

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, significantly expanding the application scenarios of FL. However, most existing DFL algorithms are based on symmetric topologies, such as ring and grid topology, which can easily lead to deadlocks and are susceptible to the impact of network link quality in practice. To address these issues, we propose DFedSGPSM, a transitional framework that converts symmetric DFL optimizers into asymmetric variants. By adopting the Push-Sum protocol in asymmetric network topologies, our framework successfully circumvents the deadlock and link-quality issues prevalent in symmetric configurations. To further validate the effectiveness of our algorithm framework, we integrate the local momentum (in DFedAvgM) and SAM (in DFedSAM) from existing symmetric DFL optimizer into DFedSGPSM to accelerate training and pursue smooth local minimum, which enables existing symmetric DFL optimizers to be seamlessly integrated into asymmetric DFL. Theoretical analysis proves that DFedSGPSM achieves a linear speedup rate of$\mathcal{O}(\frac{1}{\sqrt{nT}})$in the non-convex setting. This analysis also reveals crucial issues such as tighter upper bounds achieved with improved topological connectivity. Empirically, extensive experiments conducted on the MNIST, CIFAR10&100 datasets demonstrate the superior performance of our proposed algorithm compared to several existing SOTA optimizers in terms of generalization.

Personalized Federated Learning (PFL) is proposed to find the greatest personalized models for each client. To avoid the central failure and communication bottleneck in the server-based FL, we concentrate on the Decentralized Personalized Federated Learning (DPFL) that performs distributed model training in a Peer-to-Peer (P2P) manner. Most personalized works in DPFL are based on undi-rected and symmetric topologies, however, the data, computation and communication resources heterogeneity result in large variances in the personalized models, which lead the undirected aggregation to suboptimal personalized per-formance and unguaranteed convergence. To address these issues, we propose a directed collaboration DPFL framework by incorporating stochastic gradient push and partial model personalized, called Decentralized Federated Partial Gradient Push (DFedPGP). It personalizes the linear clas-sifier in the modern deep model to customize the local solution and learns a consensus representation in a fully de-centralized manner. Clients only share gradients with a subset of neighbors based on the directed and asymmetric topologies, which guarantees flexible choices for resource efficiency and better convergence. Theoretically, we show that the proposed DFedPGP achieves a superior conver-gence rate of O (1/√T) in the general non-convex setting, and prove the tighter connectivity among clients will speed up the convergence. The proposed method achieves state-of-the-art (SOTA) accuracy in both data and computation heterogeneity scenarios, demonstrating the efficiency of the directed collaboration and partial gradient push.