## 1 Introduction
### Motivation and Contributions  
Federated Learning (FL) [8], as an emerging distributed machine learning method, allows participants to collaboratively train a global model without sharing local data, thus enhancing model performance while protecting data privacy. However, existing federated learning algorithms, primarily designed for ground networks, are difficult to apply directly to SAGINs. Particularly in high-latency and limited-bandwidth environments, traditional federated learning algorithms often face inefficient communication and slow model convergence. Furthermore, the dynamic network topology and data heterogeneity in SAGINs further complicate model training. Therefore, how to implement efficient privacy-preserving federated learning in SAGINs has become an urgent research problem to solve. Federated Learning (FL) represents an optimal paradigm for SAGIN environments compared to alternative distributed learning approaches due to several fundamental advantages. Unlike centralized learning that requires raw data transmission across the entire network, FL minimizes communication overhead by exchanging only model updates. This is particularly crucial in SAGINs, where bandwidth constraints between layers can severely limit data exchange. Similarly, while distributed learning approaches such as parameter server architectures or decentralized learning require frequent synchronization and consistent connectivity, FL's episodic communication pattern better accommodates SAGINs' intermittent connections and dynamic topology changes. However, traditional FL frameworks face significant limitations when deployed in SAGIN environments: (1) Communication overhead remains challenging, as model updates must traverse high-latency satellite links or bandwidth-limited aerial connections; (2) Synchronization bottlenecks occur when all devices must report updates within each round, which is impractical given the varying connection durations of space and aerial nodes; (3) Device heterogeneity in SAGINs spans orders of magnitude greater than in traditional networks, making conventional aggregation algorithms ineffective; (4) Privacy vulnerabilities are amplified in SAGINs' multi-layer architecture where sensitive information can be intercepted during cross-layer transmissions. Our proposed PPFL-SAGIN framework directly addresses these limitations through several innovative mechanisms: (1) The bi-level reinforcement learning device selection strategy intelligently balances device participation across different SAGIN layers, reducing communication overhead by up to 65% compared to traditional FL; (2) Asynchronous updating with adaptive knowledge sharing mitigates synchronization challenges, enabling model convergence despite intermittent satellite or UAV connectivity; (3) Dynamic privacy budget allocation provides stronger protection for vulnerable aerial and space-based nodes while maintaining model utility. The practical relevance of PPFL-SAGINs extends to critical real-world applications. In disaster response scenarios, PPFL-SAGINs enable rapid situational awareness by allowing emergency response UAVs, satellites monitoring affected areas, and ground rescue teams to collaboratively train damage assessment models without transmitting sensitive imagery across bandwidth-limited emergency networks. For military operations, the framework supports secure collaborative intelligence analysis across strategic command centers, tactical field units, and reconnaissance platforms while maintaining operational security through differential privacy mechanisms. In remote healthcare delivery, medical devices in underserved regions can improve diagnostic models by federating with specialists' systems through satellite links, all while preserving patient privacy. These applications demonstrate how PPFL-SAGINs scale beyond simulated environments to address pressing challenges requiring coordination across space, air, and ground assets with privacy guarantees.