## 1 Introduction
To address this, we propose the Aggregated Gradient Performance Mechanism (AGPM). This novel approach optimizes gradient updates and privacy budgets to ensure strong utility and privacy preservation, thereby balancing the trade-off between privacy and utility in federated healthcare systems. The hierarchical structure is beneficial for large-scale healthcare systems, and its Differential Privacy, secure computation, encryption, and gradient perturbation provide adequate privacy with the best model performance. This study presents a novel Hierarchical Federated Learning (HFL) framework specifically tailored for large-scale, privacy-preserving machine learning in healthcare contexts where traditional FL falls short. The key aspects of the proposed HFL framework are as follows:  
1. A two-tier aggregation architecture with local, regional, and global levels to enhance scalability and reduce communication costs for large, dispersed healthcare systems. 2. Leveraging techniques like Local/Global Differential Privacy, Secure Multi-Party Computation, and Homomorphic Encryption to robustly protect patient data privacy during model training [4; 5]. 3. Introducing a new Aggregated Gradient Perturbation technique to inject less noise while still preserving strong privacy guarantees, addressing the privacy-utility trade-off. The proposed HFL framework aims to enable collaborative, privacy-preserving machine learning for healthcare that allows institutions to share insights without compromising patient privacy--a key requirement in regulated health contexts. It claims to provide advantages over existing approaches in accuracy, efficiency, privacy, and managing the privacy-utility balance. The experimental outcomes demonstrate that the developed framework has several advantages over previous works in terms of preserving privacy and model accuracy. This framework is a step toward the potential of collaborative, privacy-preserving machine learning in healthcare that will allow institutions to share mutual intelligence without compromising patients' privacy. The rest of the research study organized as follows: Section 2 provides an overview of the related work within the domain of federated learning and its related fields like data usage in healthcare, privacy and security in federated learning, privacy-preserving techniques, Differential Privacy (DP), Secure Multi-Party Computation (SMPC), Local Differential Privacy (LDP), Global Differential Privacy (GDP), Secure Multi-Party Computation (SMPC), Hierarchical Federated Learning (HFL), privacy vs. model usefulness, the Aggregated Gradient Perturbation Mechanism, and the privacy-utility trade-off. Section 3 consists of the dataset explication, further divided into sub-sections like Data Accumulation, Data Dissection and Data Preprocessing. Section 4 explains the methodological conception and execution, constitution of the architectural framework, data and computation propagation, privacy preservation mechanisms, Local Differential Privacy (LDP), Global Differential Privacy (GDP), Secure Multi-Party Computation (SMPC) and Homomorphic Encryption (HE). Section 5 presents the results of this empirical study and Section 6 presents the conclusion.