  Cloud-edge-device hierarchical federated learning (HFL) has been recently
proposed to achieve communication-efficient and privacy-preserving distributed
learning. However, there exist several critical challenges, such as the single
point of failure and potential stragglers in both edge servers and local
devices. To resolve these issues, we propose a decentralized and
straggler-tolerant blockchain-based HFL (BHFL) framework. Specifically, a
Raft-based consortium blockchain is deployed on edge servers to provide a
distributed and trusted computing environment for global model aggregation in
BHFL. To mitigate the influence of stragglers on learning, we propose a novel
aggregation method, HieAvg, which utilizes the historical weights of stragglers
to estimate the missing submissions. Furthermore, we optimize the overall
latency of BHFL by jointly considering the constraints of global model
convergence and blockchain consensus delay. Theoretical analysis and
experimental evaluation show that our proposed BHFL based on HieAvg can
converge in the presence of stragglers, which performs better than the
traditional methods even when the loss function is non-convex and the data on
local devices are non-independent and identically distributed (non-IID).
