Raffaele Iervolino

Ali Forootani, Raffaele Iervolino

Federated Learning (FL) has emerged as a powerful paradigm for decentralized machine learning, enabling collaborative model training across diverse clients without sharing raw data. However, traditional FL approaches often face limitations in scalability and efficiency due to their reliance on synchronous client updates, which can result in significant delays and increased communication overhead, particularly in heterogeneous and dynamic environments. To address these challenges in this paper, we propose an Asynchronous Federated Learning (AFL) algorithm, which allows clients to update the global model independently and asynchronously. Our key contributions include a comprehensive convergence analysis of AFL in the presence of client delays and model staleness. By leveraging martingale difference sequence theory and variance bounds, we ensure robust convergence despite asynchronous updates. Assuming strongly convex local objective functions, we establish bounds on gradient variance under random client sampling and derive a recursion formula quantifying the impact of client delays on convergence. Furthermore, we demonstrate the practical applicability of the AFL algorithm by training decentralized linear regression and Support Vector Machine (SVM) based classifiers and compare its results with synchronous FL algorithm to effectively handling non-IID data distributed among clients. The proposed AFL algorithm addresses key limitations of traditional FL methods, such as inefficiency due to global synchronization and susceptibility to client drift. It enhances scalability, robustness, and efficiency in real-world settings with heterogeneous client populations and dynamic network conditions. Our results underscore the potential of AFL to drive advancements indistributed learning systems, particularly for large-scale, privacy-preserving applications in resource-constrained environments.

Ali Forootani, Raffaele Iervolino

This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman variants-scalar-gated, per-mode gated, MLP-shaped spectral mapping, and low-rank Koopman operators which generalize and interpolate between strictly stable Koopman operators and unconstrained linear latent dynamics. Our formulation enables explicit control over the spectrum, stability, and rank of the linear transition operator while retaining compatibility with expressive nonlinear backbones such as Patchtst, Autoformer, and Informer. We evaluate the proposed operators in a large-scale benchmark that also includes LSTM, DLinear, and simple diagonal State-Space Models (SSMs), as well as lightweight transformer variants. Experiments across multiple horizons and patch lengths show that learnable Koopman models provide a favorable bias-variance trade-off, improved conditioning, and more interpretable latent dynamics. We provide a full spectral analysis, including eigenvalue trajectories, stability envelopes, and learned spectral distributions. Our results demonstrate that learnable Koopman operators are effective, stable, and theoretically principled components for deep forecasting.

Ali Forootani, Raffaele Iervolino

Federated Learning (FL) enables collaborative model training across decentralized devices while preserving data privacy. However, traditional FL suffers from communication overhead, system heterogeneity, and straggler effects. Asynchronous Federated Learning (AFL) addresses these by allowing clients to update independently, improving scalability and reducing synchronization delays. This paper extends AFL to handle non-convex objective functions and heterogeneous datasets, common in modern deep learning. We present a rigorous convergence analysis, deriving bounds on the expected gradient norm and studying the effects of staleness, variance, and heterogeneity. To mitigate stale updates, we introduce a staleness aware aggregation that prioritizes fresher updates and a dynamic learning rate schedule that adapts to client staleness and heterogeneity, improving stability and convergence. Our framework accommodates variations in computational power, data distribution, and communication delays, making it practical for real world applications. We also analyze the impact of client selection strategies-sampling with or without replacement-on variance and convergence. Implemented in PyTorch with Python's asyncio, our approach is validated through experiments demonstrating improved performance and scalability for asynchronous, heterogeneous, and non-convex FL scenarios.