# Multi-Stage Hybrid Federated Learning over Large-Scale D2D-Enabled Fog Networks

arXiv: https://arxiv.org/abs/2007.09511 · HTML: https://mlsanity.com/paper/2007.09511/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2020.

## Built on by (most cited first, 30 of 42)

- [Distributed Learning in Wireless Networks: Recent Progress and Future Challenges](https://mlsanity.com/paper/2104.02151/) (2021)
- [Semi-Decentralized Federated Learning with Cooperative D2D Local Model Aggregations](https://mlsanity.com/paper/2103.10481/) (2021)
- [Device Sampling for Heterogeneous Federated Learning: Theory, Algorithms, and Implementation](https://mlsanity.com/paper/2101.00787/) (2021)
- [Federated Learning-Empowered AI-Generated Content in Wireless Networks](https://mlsanity.com/paper/2307.07146/) (2023)
- [Topology-aware Federated Learning in Edge Computing: A Comprehensive Survey](https://mlsanity.com/paper/2302.02573/) (2023)
- [UAV-assisted Online Machine Learning over Multi-Tiered Networks: A Hierarchical Nested Personalized Federated Learning Approach](https://mlsanity.com/paper/2106.15734/) (2021)
- [Parallel Successive Learning for Dynamic Distributed Model Training over Heterogeneous Wireless Networks](https://mlsanity.com/paper/2202.02947/) (2022)
- [Latency Optimization for Blockchain-Empowered Federated Learning in Multi-Server Edge Computing](https://mlsanity.com/paper/2203.09670/) (2022)
- [Filling the Missing: Exploring Generative AI for Enhanced Federated Learning over Heterogeneous Mobile Edge Devices](https://mlsanity.com/paper/2310.13981/) (2023)
- [Autonomy and Intelligence in the Computing Continuum: Challenges, Enablers, and Future Directions for Orchestration](https://mlsanity.com/paper/2205.01423/) (2022)
- [Opportunistic Federated Learning: An Exploration of Egocentric Collaboration for Pervasive Computing Applications](https://mlsanity.com/paper/2103.13266/) (2021)
- [Multi-Edge Server-Assisted Dynamic Federated Learning with an Optimized Floating Aggregation Point](https://mlsanity.com/paper/2203.13950/) (2022)
- [Hierarchical Federated Learning in Wireless Networks: Pruning Tackles Bandwidth Scarcity and System Heterogeneity](https://mlsanity.com/paper/2308.01562/) (2023)
- [Decentralized Event-Triggered Federated Learning with Heterogeneous Communication Thresholds](https://mlsanity.com/paper/2204.03726/) (2022)
- [Non-Coherent Over-the-Air Decentralized Gradient Descent](https://mlsanity.com/paper/2211.10777/) (2022)
- [Delay-Aware Hierarchical Federated Learning](https://mlsanity.com/paper/2303.12414/) (2023)
- [Hierarchical Federated Learning with Multi-Timescale Gradient Correction](https://mlsanity.com/paper/2409.18448/) (2024)
- [FedFog: Network-Aware Optimization of Federated Learning over Wireless Fog-Cloud Systems](https://mlsanity.com/paper/2107.02755/) (2021)
- [Federated Learning for Cyber Physical Systems: A Comprehensive Survey](https://mlsanity.com/paper/2505.04873/) (2025)
- [The Gradient Convergence Bound of Federated Multi-Agent Reinforcement Learning with Efficient Communication](https://mlsanity.com/paper/2103.13026/) (2021)
- [Embedding Alignment for Unsupervised Federated Learning via Smart Data Exchange](https://mlsanity.com/paper/2208.02856/) (2022)
- [Social-Aware Clustered Federated Learning with Customized Privacy Preservation](https://mlsanity.com/paper/2212.13992/) (2022)
- [Analog-digital Scheduling for Federated Learning: A Communication-Efficient Approach](https://mlsanity.com/paper/2402.00318/) (2024)
- [A Multi-Token Coordinate Descent Method for Semi-Decentralized Vertical Federated Learning](https://mlsanity.com/paper/2309.09977/) (2023)
- [Management of Resource at the Network Edge for Federated Learning](https://mlsanity.com/paper/2107.03428/) (2021)
- [On Differential Privacy for Federated Learning in Wireless Systems with Multiple Base Stations](https://mlsanity.com/paper/2208.11848/) (2022)
- [Biased Over-the-Air Federated Learning under Wireless Heterogeneity](https://mlsanity.com/paper/2403.19849/) (2024)
- [UAV-assisted Unbiased Hierarchical Federated Learning: Performance and Convergence Analysis](https://mlsanity.com/paper/2407.07739/) (2024)
- [Does Worst-Performing Agent Lead the Pack? Analyzing Agent Dynamics in Unified Distributed SGD](https://mlsanity.com/paper/2409.17499/) (2024)
- [Hierarchical Federated Foundation Models over Wireless Networks for Multi-Modal Multi-Task Intelligence: Integration of Edge Learning with D2D/P2P-Enabled Fog Learning Architectures](https://mlsanity.com/paper/2509.03695/) (2025)

## Abstract (arXiv)

Federated learning has generated significant interest, with nearly all works focused on a "star" topology where nodes/devices are each connected to a central server. We migrate away from this architecture and extend it through the network dimension to the case where there are multiple layers of nodes between the end devices and the server. Specifically, we develop multi-stage hybrid federated learning (MH-FL), a hybrid of intra- and inter-layer model learning that considers the network as a multi-layer cluster-based structure. MH-FL considers the topology structures among the nodes in the clusters, including local networks formed via device-to-device (D2D) communications, and presumes a semi-decentralized architecture for federated learning. It orchestrates the devices at different network layers in a collaborative/cooperative manner (i.e., using D2D interactions) to form local consensus on the model parameters and combines it with multi-stage parameter relaying between layers of the tree-shaped hierarchy. We derive the upper bound of convergence for MH-FL with respect to parameters of the network topology (e.g., the spectral radius) and the learning algorithm (e.g., the number of D2D rounds in different clusters). We obtain a set of policies for the D2D rounds at different clusters to guarantee either a finite optimality gap or convergence to the global optimum. We then develop a distributed control algorithm for MH-FL to tune the D2D rounds in each cluster over time to meet specific convergence criteria. Our experiments on real-world datasets verify our analytical results and demonstrate the advantages of MH-FL in terms of resource utilization metrics.