Byzantine attacks present a critical challenge to Federated Learning (FL), where malicious participants can disrupt the training process, degrade model accuracy, and compromise system reliability. Traditional FL frameworks typically rely on aggregation-based protocols for model updates, leaving them vulnerable to sophisticated adversarial strategies. In this paper, we demonstrate that distributed optimization offers a principled and robust alternative to aggregation-centric methods. Specifically, we show that the Primal-Dual Method of Multipliers (PDMM) inherently mitigates Byzantine impacts by leveraging its fault-tolerant consensus mechanism. Through extensive experiments on three datasets (MNIST, FashionMNIST, and Olivetti), under various attack scenarios including bit-flipping and Gaussian noise injection, we validate the superior resilience of distributed optimization protocols. Compared to traditional aggregation-centric approaches, PDMM achieves higher model utility, faster convergence, and improved stability. Our results highlight the effectiveness of distributed optimization in defending against Byzantine threats, paving the way for more secure and resilient federated learning systems.

Federated Learning (FL) enables collaborative learning without directly sharing individual's raw data. FL can be implemented in either a centralized (server-based) or decentralized (peer-to-peer) manner. In this survey, we present a novel perspective: the fundamental difference between centralized FL (CFL) and decentralized FL (DFL) is not merely the network topology, but the underlying training protocol: separate aggregation vs. joint optimization. We argue that this distinction in protocol leads to significant differences in model utility, privacy preservation, and robustness to attacks. We systematically review and categorize existing works in both CFL and DFL according to the type of protocol they employ. This taxonomy provides deeper insights into prior research and clarifies how various approaches relate or differ. Through our analysis, we identify key gaps in the literature. In particular, we observe a surprising lack of exploration of DFL approaches based on distributed optimization methods, despite their potential advantages. We highlight this under-explored direction and call for more research on leveraging distributed optimization for federated learning. Overall, this work offers a comprehensive overview from centralized to decentralized FL, sheds new light on the core distinctions between approaches, and outlines open challenges and future directions for the field.

Federated learning (FL) emerged as a paradigm designed to improve data privacy by enabling data to reside at its source, thus embedding privacy as a core consideration in FL architectures, whether centralized or decentralized. Contrasting with recent findings by Pasquini et al., which suggest that decentralized FL does not empirically offer any additional privacy or security benefits over centralized models, our study provides compelling evidence to the contrary. We demonstrate that decentralized FL, when deploying distributed optimization, provides enhanced privacy protection - both theoretically and empirically - compared to centralized approaches. The challenge of quantifying privacy loss through iterative processes has traditionally constrained the theoretical exploration of FL protocols. We overcome this by conducting a pioneering in-depth information-theoretical privacy analysis for both frameworks. Our analysis, considering both eavesdropping and passive adversary models, successfully establishes bounds on privacy leakage. We show information theoretically that the privacy loss in decentralized FL is upper bounded by the loss in centralized FL. Compared to the centralized case where local gradients of individual participants are directly revealed, a key distinction of optimization-based decentralized FL is that the relevant information includes differences of local gradients over successive iterations and the aggregated sum of different nodes' gradients over the network. This information complicates the adversary's attempt to infer private data. To bridge our theoretical insights with practical applications, we present detailed case studies involving logistic regression and deep neural networks. These examples demonstrate that while privacy leakage remains comparable in simpler models, complex models like deep neural networks exhibit lower privacy risks under decentralized FL.