The rise of distributed machine learning has opened the door to collaborative solutions that optimize computational resources and data privacy. Among these, the Federated Averaging Algorithm (FedAvg) has emerged as a key methodology for performing decentralized optimization of machine learning models. This paper aims to explore the foundational framework of FedAvg, its practical applications, and limitations. A comprehensive understanding of FedAvg contributes to the development of more efficient and privacy-preserving machine learning algorithms. Keywords: Federated Learning, FedAvg, Machine Learning, Distributed Computing, Privacy Introduction As the need for data-driven solutions becomes increasingly prominent, traditional centralized machine learning models are often found to be impractical or even infeasible due to issues such as data privacy and computational inefficiency. Federated Learning (FL), a distributed machine learning paradigm, has come to the fore to address these challenges. The Federated Averaging Algorithm (FedAvg) is one of the pivotal algorithms used in FL, facilitating the training of machine learning models across multiple decentralized devices or servers (McMahan et al., 2017). This paper examines the underlying framework, applications, and limitations of the FedAvg algorithm. Theoretical Framework Algorithmic Foundations FedAvg essentially extends the Stochastic Gradient Descent (SGD) algorithm to a distributed context. At a high level, each participating device computes its own local model updates based on its local data. Subsequently, these local updates are averaged to produce a global model update (McMahan et al., 2017). Mathematically, the algorithm can be defined by the following update rule: 𝑤𝑔𝑙𝑜𝑏𝑎𝑙 = ∑𝑛𝑘 𝑤𝑘/𝑛 Where w_global is the global model parameter, w_k represents the local model parameter for the k-th device, n_k is the number of data points on the k-th device, n is the total number of data points, and K is the number of devices. Privacy Considerations FedAvg inherently offers some level of data privacy as raw data does not need to be shared with a centralized server. However, the algorithm alone does not guarantee full privacy, and additional techniques like Differential Privacy may be required (Abadi et al., 2016). Applications Healthcare In healthcare, federated learning and the FedAvg algorithm have shown promise in aggregating information across multiple institutions without sharing sensitive patient data (Brisimi et al., 2018). Internet of Things (IoT) FedAvg is particularly useful in IoT ecosystems where devices like sensors and smart appliances can benefit from machine learning without sending sensitive data to a centralized cloud server (Leroy et al., 2019). Limitations Communication Overhead Despite its advantages, FedAvg suffers from high communication overhead as model parameters have to be communicated to a central server for averaging. Non-IID Data The algorithm's efficiency is also impacted when the data is not identically and independently distributed across devices (Zhao et al., 2018). Conclusion The Federated Averaging Algorithm has been a cornerstone in federated learning, enabling decentralized machine learning that is both resource-efficient and privacy-preserving. However, challenges such as communication overhead and non-IID data remain to be addressed. Further research is needed to augment FedAvg with solutions that can mitigate these limitations.