Federated Learning (FL) is a distributed machine learning approach that enables training on decentralized data while preserving privacy. However, FL systems often involve resource-constrained client devices with limited computational power, memory, storage, and bandwidth. This paper introduces FedMap, a novel method that aims to enhance the communication efficiency of FL deployments by collaboratively learning an increasingly sparse global model through iterative, unstructured pruning. Importantly, FedMap trains a global model from scratch, unlike other methods reported in the literature, making it ideal for privacy-critical use cases such as in the medical and finance domains, where suitable pre-training data is often limited. FedMap adapts iterative magnitude-based pruning to the FL setting, ensuring all clients prune and refine the same subset of the global model parameters, therefore gradually reducing the global model size and communication overhead. The iterative nature of FedMap, forming subsequent models as subsets of predecessors, avoids parameter reactivation issues seen in prior work, resulting in stable performance. In this paper we provide an extensive evaluation of FedMap across diverse settings, datasets, model architectures, and hyperparameters, assessing performance in both IID and non-IID environments. Comparative analysis against the baseline approach demonstrates FedMap's ability to achieve more stable client model performance. For IID scenarios, FedMap achieves over $90$\% pruning without significant performance degradation. In non-IID settings, it achieves at least $~80$\% pruning while maintaining accuracy. FedMap offers a promising solution to alleviate communication bottlenecks in FL systems while retaining model accuracy.

Federated Learning (FL) enables collaborative training of machine learning models on decentralized data while preserving data privacy. However, data across clients often differs significantly due to class imbalance, feature distribution skew, sample size imbalance, and other phenomena. Leveraging information from these not identically distributed (non-IID) datasets poses substantial challenges. FL methods based on a single global model cannot effectively capture the variations in client data and underperform in non-IID settings. Consequently, Personalized FL (PFL) approaches that adapt to each client's data distribution but leverage other clients' data are essential but currently underexplored. We propose a novel Bayesian PFL framework using bi-level optimization to tackle the data heterogeneity challenges. Our proposed framework utilizes the global model as a prior distribution within a Maximum A Posteriori (MAP) estimation of personalized client models. This approach facilitates PFL by integrating shared knowledge from the prior, thereby enhancing local model performance, generalization ability, and communication efficiency. We extensively evaluated our bi-level optimization approach on real-world and synthetic datasets, demonstrating significant improvements in model accuracy compared to existing methods while reducing communication overhead. This study contributes to PFL by establishing a solid theoretical foundation for the proposed method and offering a robust, ready-to-use framework that effectively addresses the challenges posed by non-IID data in FL.