Convergence Analysis of Sequential Federated Learning on Heterogeneous Data

Federated Learning (FL) has emerged as a promising solution for data hunger in centralized learning. This paradigm enables privacy with multiple clients to train a shared-task model collaboratively without exposing their local data. While being a key component in any learning system, data is also a primary source of vulnerabilities and challenges, and a major determinant of a stable and well-converged training. Existing FL reviews describe general foundations, security practices, opportunities, challenges, and applications, without delving into diverse aspects of data and considering problems from the data perspective. They rarely provide a data-lens synthesis that links concrete data properties, split protocols, and defenses to convergence speed and stability. This survey fills that gap with three advances. First, we analyze non-IID into measurable traits and rank their influence on convergence as strong, medium, or light, explaining the mechanisms behind each and reconciling evidence across images, texts, and graphs. Second, we connect experimental splitting practices to the real phenomena they emulate, expose the artifacts they introduce, and show how those artifacts affect target accuracy. Third, we analyze how data-related vulnerabilities and their proposed defenses affect convergence, reporting performance under clean and adversarial conditions to make the convergence-robustness trade-off explicit. To our knowledge, this is the first survey to provide a complete understanding of data-related challenges that govern FL. With clear takeaways distilled for each concern, our work serves as actionable guidance, helping practitioners design their system with predictable convergence and stability.

We consider Decision-Focused Federated Learning (DFFL), a predict-then-optimize setting in which multiple clients collaboratively train predictive models for downstream linear optimization problems without exchanging raw data. Besides the data heterogeneity typical of standard federated learning, clients may also have different objective functions and feasible regions. Building on the SPO+ surrogate loss, we derive heterogeneity bounds that separate objective shift, measured through cost-vector distances, from feasible-set shift, measured through support-function and shape-distance terms. We show that, for general compact feasible sets, small objective perturbations can still induce nonvanishing decision-focused loss discrepancies, while strongly convex feasible regions yield sharper stability-based bounds. We then lift these pointwise bounds to a local-versus-federated excess-risk comparison, showing that federation is beneficial when the statistical advantage of pooling exceeds a client-specific heterogeneity penalty. Computational experiments on polyhedral and strongly convex problems confirm that federation is substantially more robust under strongly convex feasible regions. Finally, we evaluate a simple validation-based interpolation between local and federated DFFL models. This interpolation mitigates the theoretical tradeoff and reduces aggregate regret and worst-client harm in both synthetic experiments and a PJM energy-pricing case study.

Federated Learning (FL) has gained significant attention in distributed machine learning by enabling collaborative model training across decentralized system while preserving data privacy. Although extensive research has addressed statistical data heterogeneity, FL still faces several challenges, including high communication and computation overheads and severe device heterogeneity, which require further investigation. Prior work has addressed these issues through sub-model training and partial parameter training. However, such methods often suffer from inconsistent parameter distributions across clients, inaccurate global loss estimation, and increased bias and variance. Guided by our empirical analysis, we propose FedPLT (Federated Learning with Partial Layer Training), an innovative and structured partial parameter training approach that exhibits training behavior similar to full model training while assigning client-specific portions of the model according to their communication and computational capabilities. In addition, we evaluate the performance of FedPLT when combined with optimal client sampling under communication constraints. We show that this integration improves FL performance by reducing sampling variance under the same communication budget. Through extensive experiments, we demonstrate that FedPLT achieves performance comparable to, or even surpassing, that of full-model training (i.e., FedAvg), while requiring significantly fewer trainable parameters per client. Moreover, FedPLT outperforms existing methods in highly heterogeneous environments, effectively adapts to client resource constraints, and reduces the number of straggling clients. In particular, FedPLT reduces the number of trainable parameters by 71%-82% while achieving performance on par with full-model training.