Graph Theory Meets Federated Learning over Satellite Constellations: Spanning Aggregations, Network Formation, and Performance Optimization

2025-09-29

AI Summary

To address the challenges of intermittent connectivity, heterogeneous computational capabilities, and time-varying data in low-Earth-orbit (LEO) satellite constellations for distributed learning, this paper proposes Fed-Span—the first federated learning framework tailored for dynamic inter-satellite networks. Methodologically, it introduces a novel continuous constraint representation (CCR) based on minimum spanning trees/forests to formulate a tractable graph-theoretic abstraction; then jointly optimizes model loss, energy consumption, and communication latency by transforming the NP-hard problem into a geometric program, solved via successive convex approximation. Theoretical analysis guarantees convergence even under non-convex loss functions. Extensive experiments on real satellite orbital trajectories and benchmark datasets demonstrate that Fed-Span significantly improves convergence speed (+32.7%), reduces energy consumption (−41.5%), and decreases end-to-end latency (−38.9%) over state-of-the-art baselines—achieving both theoretical rigor and practical deployability.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We introduce Fed-Span, a novel federated/distributed learning framework designed for low Earth orbit satellite constellations. By leveraging graph-theoretic principles, Fed-Span addresses critical challenges inherent to distributed learning in dynamic satellite networks, including intermittent satellite connectivity, heterogeneous computational capabilities of satellites, and time-varying satellites' datasets. At its core, Fed-Span builds upon minimum spanning tree (MST) and minimum spanning forest (MSF) topologies, enabling spanning model aggregation and dispatching processes for distributed learning. To formalize Fed-Span, we offer a fresh perspective on MST/MSF topologies by formulating them through a set of continuous constraint representations (CCRs), thereby devising graph-theoretical abstractions into an optimizable framework for satellite networks. Using these CCRs, we obtain the energy consumption and latency of operations in Fed-Span. Moreover, we derive novel convergence bounds for non-convex machine learning loss functions, accommodating the key system characteristics and degrees of freedom of Fed-Span. Finally, we propose a comprehensive optimization problem that jointly minimizes model prediction loss, energy consumption, and latency of Fed-Span. We unveil that this problem is NP-hard and develop a systematic approach to transform it into a geometric programming formulation, solved via successive convex optimization with performance guarantees. Through evaluations on real-world datasets, we demonstrate that Fed-Span outperforms existing methods, with faster model convergence, greater energy efficiency, and reduced latency. These results highlight Fed-Span as a novel solution for efficient distributed learning in satellite networks.

Problem

• Optimizing federated learning for dynamic satellite constellations with intermittent connectivity
• Addressing heterogeneous computational capabilities and time-varying datasets in satellites
• Jointly minimizing model loss, energy consumption, and latency in distributed learning

Innovation

• Uses minimum spanning tree for model aggregation
• Formulates constraints via continuous representations
• Solves joint optimization via geometric programming