## 2 Background
### Communication
On the server, an aggregation process takes place, where these gradients from multiple devices are combined to update the global model. This approach not only safeguards individual data confidentiality but also facilitates the integration of heterogeneous datasets into a unified model. By aggregating diverse local updates, Federated SGD harnesses the collective intelligence embedded in disparate data sources, enhancing the robustness and relevance of the global model. * Bandwidth optimization and application versatility The reduction in data transmission volume inherent to Federated SGD addresses the challenges posed by restricted bandwidth environments. In traditional centralized learning models, the transmission of large volumes of raw data can be a significant bottleneck, consuming substantial network resources. Federated SGD elegantly circumvents this issue by transmitting only essential gradient information, thereby optimizing bandwidth usage. This optimization is crucial for ensuring the scalability and efficiency of FLSs, particularly when deployed in bandwidth-constrained settings. Furthermore, the versatility of Federated SGD extends its applicability across a broad spectrum of domains. From healthcare to finance, and from mobile computing to Internet of Things (IoT) applications, this methodology proves instrumental in diverse fields by facilitating effective model training across various scenarios while maintaining data privacy and minimizing risk. * Federated Averaging with Momentum (FedAvgM): represents a significant enhancement over the traditional Federated Averaging (FedAvg) algorithm, primarily used in Federated Learning Systems (FLSs). This advanced algorithm introduces a momentum component to the model updates, enhancing the overall efficiency and accuracy of the learning process. FedAvgM not only leverages the collaborative capabilities inherent in Federated Learning but also introduces the stability and efficiency offered by momentum-based optimization. This results in a more robust and responsive learning algorithm capable of adapting to the nuanced requirements of distributed learning scenarios. The central innovation in FedAvgM lies in the incorporation of a velocity component, or momentum, into the model updates. This momentum term allows the algorithm to'remember' and integrate a portion of the previous update into the current one. * Enhanced convergence and optimization: By maintaining its previous trajectory through the velocity term, FedAvgM accelerates the convergence process. This momentum-driven approach is particularly beneficial in scenarios with non-IID data distributions or significant data volatility, where traditional FedAvg might struggle with slow or unstable convergence. * Application in diverse scenarios: FedAvgM demonstrates remarkable effectiveness in a variety of distributed environments. Its ability to facilitate rapid and steady knowledge acquisition across distributed devices makes it an ideal choice for FLSs dealing with complex data landscapes. The algorithm effectively balances the need for accurate and efficient model training while maintaining user privacy and data security. In summary, Federated Averaging with Momentum elevates the traditional Federated Learning approach by introducing a dynamic and adaptive component that significantly enhances model training effectiveness. Its ability to handle complex data distributions and volatile environments, while ensuring rapid convergence and optimization, marks it as a valuable tool in the realm of Federated Learning. The inclusion of momentum in the federated averaging with momentum optimization algorithm enhances the traditional federated averaging approach in FLSs. This modification introduces a velocity component into model updates, enabling the algorithm to maintain its previous trajectory while accelerating, resulting in faster convergence and improved optimization.