Hierarchical Asynchronous Federated Learning over Space-Air-Ground Integrated Networks

Kai Wang; Chee Wei Tan

cs.LGOct 31, 2026

Hierarchical Asynchronous Federated Learning over Space-Air-Ground Integrated Networks

Authors: Kai Wang, Chee Wei Tan

Organizations: College of Computing and Data Science, Nanyang Technological University, Singapore 639798

Abstract

With the emerging 6G paradigm where AI services operate over decentralized and resource-constrained edge infrastructure, performance of distributed learning algorithms remains a significant challenge. This paper proposes HAFL, a Low Earth Orbit (LEO) satellite-assisted hierarchical asynchronous Federated Learning (FL) framework, enabling resource-limited terrestrial clients to collaborate via Ground-Satellite Links (GSLs). Within this framework, LEO satellites serve multiple roles: as edge servers aggregating and broadcasting models, as clients accelerating training, and as high-throughput relays managing inter-satellite routing through Inter-Satellite Links (ISLs). Unlike conventional synchronous Jacobian-type updates, HAFL employs asynchronous Gauss-Seidel-type updates to enhance convergence speed. We provide theoretical convergences for convex, strongly convex, and nonconvex objectives, respectively, and formulate optimization problems to jointly determine optimal hyperparameters to minimize global training latency. Evaluations demonstrate that HAFL achieves faster initial convergence and comparable final performance for benchmark DNNs and datasets, offering promising FL systems across remote areas with 6G technologies, but much less global rounds and communication cost.

Figures & tables

Fig. 1: An illustration of the submodel transmission scheme. In this scheme, solid lines denote transmission in Stage Two, and dotted lines denote transmission in Stage Three. For example, cluster 2 needs

S^{1}_{1}

to train

S^{2}_{2}

and hence

S^{1}_{1}

must be transmitted before

t=2

, corresponding to Stage Two. However, cluster 3 needs

S^{1}_{1}

to train

S^{3}_{3}

, which is time-insensitive and can be arranged to transmit during training, corresponding to Stage Three.

	$\displaystyle T^{\text{total}}_{i}=\begin{cases}T\cdot N_{i}+\max_{j\in\mathcal{C}_{i}}\big\{\tau^{\text{agg}}_{C,j}\big\},&\text{ (case$ a $)$ \qquad\qquad\qquad\qquad\qquad\qquad\qquad $}\\ \max_{j\in C_{i}}\big\{\max\big(T\cdot\big\lfloor\dfrac{T^{\text{cluster}}_{C,j^{\prime}}}{T}\big\rfloor,T^{\text{cluster}}_{C,j}\big)+\tau^{\text{agg}}_{C,j}\big\},&\text{ (case$ b $)$ \qquad\qquad\qquad\qquad\qquad\qquad\qquad $}\\ T\cdot\big(\big\lfloor\dfrac{T^{\text{cluster}}_{C,j^{\prime}}}{T}\big\rfloor+1\big)+\max_{j\in C_{i}}\big\{\tau^{\text{agg}}_{C,j}\big\},&\text{ (case$ c $)$ \qquad\qquad\qquad\qquad\qquad\qquad\qquad $}\end{cases}\qquad$		(14)
	$\displaystyle\begin{cases}\text{case$ a $:}&T^{\text{cluster}}_{C,j^{\prime}}\leq T\cdot N_{i}\\ \text{case$ b $:}&T^{\text{cluster}}_{C,j^{\prime}}>T\cdot N_{i}\text{ and }\max_{j\in C_{i}}\big\{\max\big(T\cdot\big\lfloor\dfrac{T^{\text{cluster}}_{C,j^{\prime}}}{T}\big\rfloor,T^{\text{cluster}}_{C,j}\big)\!+\!\tau^{\text{agg}}_{C,j}\big\}\!\leq\!T\cdot\big(\big\lfloor\dfrac{T^{\text{cluster}}_{C,j^{\prime}}}{T}\big\rfloor\!+\!1\big)\\ \text{case$ c $:}&T^{\text{cluster}}_{C,j^{\prime}}>T\cdot N_{i}\text{ and }\max_{j\in C_{i}}\big\{\max\big(T\cdot\big\lfloor\dfrac{T^{\text{cluster}}_{C,j^{\prime}}}{T}\big\rfloor,T^{\text{cluster}}_{C,j}\big)\!+\!\tau^{\text{agg}}_{C,j}\big\}\!>\!T\cdot\big(\big\lfloor\dfrac{T^{\text{cluster}}_{C,j^{\prime}}}{T}\big\rfloor\!+\!1\big)\end{cases}$		(15)

Table 2

Parameter	Value	Parameter	Value	Parameter	Value
$f_{S,i}$	$1$ GHz	$m_{S,i}$	$3\times 10^{7}$ cycles/sample	$P_{S,i}$	$10$ W
$f_{C,j}$	$3\times 10^{8}$ Hz	$m_{C,j}$	$3\times 10^{7}$ cycles/sample	$P_{C,j}$	$0.3$ W
$T$	$360$ sec	$\xi$	$2$	$N_{0}$	$3.98\times 10^{-21}$ W/Hz
$\kappa$	$10^{-28}$ Joules $\cdot$ seconds 2 /cycles 3	$B_{i}$	$10$ MHz	$\gamma_{S,i},\gamma_{C,j}$	$0.05$

TABLE I: Simulation Setting

Fig. 2: Jacobian and Gauss-Seidel updates for Crammer-Singer SVM with

T=50

under i.i.d. and non-i.i.d., respectively. Upper left: i.i.d. and

E=20

, upper right: i.i.d. and

H=20

, lower left: non-i.i.d. and

E=20

, lower right: non-i.i.d. and

H=20

Fig. 3: Jacobian and Gauss-Seidel updates for ResNet-18 with

T=50

under i.i.d. and non-i.i.d., respectively. Upper left: i.i.d. and

E=20

, upper right: i.i.d. and

H=20

, lower left: non-i.i.d. and

E=20

, lower right: non-i.i.d. and

H=20

ResNet-18 on Fashion-MNIST
	Fully i.i.d.		Cell non-i.i.d., client i.i.d.
	3 Cells	5 Cells	3 Cells	5 Cells
Accuracy	HAFL / HFedAvg	HAFL / HFedAvg	HAFL / HFedAvg	HAFL / HFedAvg
70%	1, 89.70 / 3, 234.00	1, 58.50 / 5, 234.00	1, 448.50 / 3, 234.00	1, 58.50 / 3, 140.40
80%	3, 269.10 / 5, 390.00	2, 117.00 / 6, 280.80	5, 538.20 / 8, 624.00	3, 175.50 / 6, 280.80

TABLE II: Global rounds and total per-client satellite-client communication cost (MB) for achieving testing accuracy of 70% and 80% on Fashion-MNIST with ResNet-18, respectively.

Fig. 4: Gauss-Seidel updates for ResNet-18 with

T=50

E=20

H=20

under i.i.d. and non-i.i.d., respectively.

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ParaBlock++: Communication-Computation Parallel Blockwise Hierarchical Federated Learning

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College of Computing and Data Science, Nanyang Technological University, Singapore 639798

Block Coordinate Descent Federated Learning Hierarchical Federated Learning Communication-Efficient Distributed Training Asynchronous Federated Learning

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In the emerging 6G paradigm, where AI-driven services operate over decentralized and resource-constrained infrastructures, the convergence of distributed learning algorithms remains a significant challenge. This paper introduces

\mathrm{ParaBlock}

++, a low Earth orbit (LEO) satellite-assisted hierarchical federated learning (HFL) framework, enabling resource-limited terrestrial clients to collaboratively engage in federated learning (FL) via ground-satellite links (GSLs) supported by LEO satellite megaconstellations. Within this architecture, LEO satellites serve multiple roles: as edge servers aggregating and broadcasting models, as clients accelerating training, and as high-throughput relays managing inter-satellite routing through inter-satellite links (ISLs). Departing from conventional synchronous Jacobian-type updates,

\mathrm{ParaBlock}

++ employs asynchronous BCD-type updates to enhance convergence speed. We provide theoretical convergence guarantees for convex, strongly convex, and non-convex objectives, and formulate optimization problems to determine optimal cluster resource allocation and model partitioning for minimizing global training latency. Experimental evaluations demonstrate that

\mathrm{ParaBlock}

++ achieves faster initial convergence and comparable final performance for deep neural networks (DNNs) such as ResNet-18, offering promising directions for federated learning across geographically remote areas enabled by 6G technologies, but much less global rounds and communication cost.

Abstract

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