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 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, 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 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.
\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 1
Fig. 1: An illustration of the submodel transmission scheme. Solid lines denote the transmission stage and dotted lines denote the propagation stage. For example, cluster 2 needs S11 to train S22 at t=2 and hence S11 must be received before t=2 , corresponding to the transmission stage. Although cluster 3 also needs S11 to train S33 at t=3 , it is time-insensitive and can be received during training at t=2 , corresponding to the propagation stage.
Parameter
Value
Parameter
Value
Parameter
Value
fS,i
1 GHz
mS,i†
3×107 cycles/sample
PS,i
10 W
fC,j
3×108 Hz
mC,j†
3×107 cycles/sample
PC,j
0.3 W
T
360 sec
ξ
2
N0
3.98×10−21 W/Hz
κ
10−28 Joules ⋅ seconds 2 /cycles 3
Bi
10 MHz
−
−
TABLE I: Simulation Settings for the LEO Megaconstellation
Fig. 2: Comparison for LR with default hyperparameters: balanced partition, T=50 , E=5 , H=10 , #clusters=4 , #clients_per_cluster=2 , αinter=10.0 , αintra=3.0 , αt=0.01/(t+1) and batch size b=32 . Upper left: varying E and H , upper right: varying #clients_per_cluster , lower left: varying αinter and αintra , lower right: varying partition balance and αt .
Fig. 3: Comparison for Crammer-Singer SVM with the same default parameters and subplots as for LR.
Fig. 4: Comparison for ResNet-18 with the same default parameters and subplots as for LR.
Model
Avg. Comp. Time
Avg. Comm. Time
ParaBlock ++
∑i∈ITˉicomp
Tstsp
HIST/FedBCD
∑i∈ITˉicomp
maxi∈ITidst
TABLE II: Computation-Communication Time Per Global Round
Fig. 5: ParaBlock ++ for ResNet-18 with T=50 , E=20 , H=20 under i.i.d. and non-i.i.d., respectively.