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Hierarchical Federated Learning with Quantization: Convergence Analysis and System Design

arXiv 2103.14272 ↗First posted 26 Mar 2021cs.LGcited by 47

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Abstract (arXiv)

Federated learning (FL) is a powerful distributed machine learning framework where a server aggregates models trained by different clients without accessing their private data. Hierarchical FL, with a client-edge-cloud aggregation hierarchy, can effectively leverage both the cloud server's access to many clients' data and the edge servers' closeness to the clients to achieve a high communication efficiency. Neural network quantization can further reduce the communication overhead during model uploading. To fully exploit the advantages of hierarchical FL, an accurate convergence analysis with respect to the key system parameters is needed. Unfortunately, existing analysis is loose and does not consider model quantization. In this paper, we derive a tighter convergence bound for hierarchical FL with quantization. The convergence result leads to practical guidelines for important design problems such as the client-edge aggregation and edge-client association strategies. Based on the obtained analytical results, we optimize the two aggregation intervals and show that the client-edge aggregation interval should slowly decay while the edge-cloud aggregation interval needs to adapt to the ratio of the client-edge and edge-cloud propagation delay. Simulation results shall verify the design guidelines and demonstrate the effectiveness of the proposed aggregation strategy.

Key facts. Cited by 47 papers in the map (data through 7 Oct 2026). Builds on 23 of its 37 references that are in the map. First posted on arXiv 26 Mar 2021.

Builds on

23 of 37 references.

References · 23

  1. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,592
  2. 2016Federated Learning: Strategies for Improving Communication Efficiencycited by 1,461
  3. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,140
  4. 2020Ensemble Distillation for Robust Model Fusion in Federated Learningcited by 678
  5. 2018Local SGD Converges Fast and Communicates Littlecited by 595
  6. 2018Federated Learning for Mobile Keyboard Predictioncited by 565
  7. 2018Adaptive Federated Learning in Resource Constrained Edge Computing Systemscited by 408
  8. 2019FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantizationcited by 349
  9. 2019Tighter Theory for Local SGD on Identical and Heterogeneous Datacited by 266
  10. 2019Client-Edge-Cloud Hierarchical Federated Learningcited by 202
  11. 2017Gradient Sparsification for Communication-Efficient Distributed Optimizationcited by 199
  12. 2020Federated Learning with Compression: Unified Analysis and Sharp Guaranteescited by 159
11 more
  1. 2018ATOMO: Communication-efficient Learning via Atomic Sparsificationcited by 135
  2. 2018Cooperative SGD: A unified Framework for the Design and Analysis of Communication-Efficient SGD Algorithmscited by 106
  3. 2020Communication-Efficient Edge AI: Algorithms and Systemscited by 95
  4. 2018Towards an Intelligent Edge: Wireless Communication Meets Machine Learningcited by 94
  5. 2018Adaptive Communication Strategies to Achieve the Best Error-Runtime Trade-off in Local-Update SGDcited by 76
  6. 2020HFEL: Joint Edge Association and Resource Allocation for Cost-Efficient Hierarchical Federated Edge Learningcited by 74
  7. 2019Device Scheduling with Fast Convergence for Wireless Federated Learningcited by 46
  8. 2019High-Dimensional Stochastic Gradient Quantization for Communication-Efficient Edge Learningcited by 32
  9. 2019Mobile Edge Intelligence and Computing for the Internet of Vehiclescited by 22
  10. 2016Delay-Optimal Computation Task Scheduling for Mobile-Edge Computing Systemscited by 10
  11. 2019A Distributed Hierarchical SGD Algorithm with Sparse Global Reductioncited by 2

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Citing papers per year: 2022: 3; 2023: 8; 2024: 20; 2025: 8; 2026: 8.

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  1. 2024Mobile Edge Intelligence for Large Language Models: A Contemporary Surveycited by 125
  2. 2024Hierarchical Split Federated Learning: Convergence Analysis and System Optimizationcited by 38
  3. 2023Green Edge AI: A Contemporary Surveycited by 24
  4. 2022Scalable Hierarchical Over-the-Air Federated Learningcited by 14
  5. 2024The Federation Strikes Back: A Survey of Federated Learning Privacy Attacks, Defenses, Applications, and Policy Landscapecited by 13
  6. 2022Predictive GAN-powered Multi-Objective Optimization for Hybrid Federated Split Learningcited by 11
  7. 2024Mobility Accelerates Learning: Convergence Analysis on Hierarchical Federated Learning in Vehicular Networkscited by 11
  8. 2024Training Machine Learning models at the Edge: A Surveycited by 11
  9. 2023Adaptive Federated Pruning in Hierarchical Wireless Networkscited by 10
  10. 2023Over-the-Air Federated Learning and Optimizationcited by 10
  11. 2024Satellite Federated Edge Learning: Architecture Design and Convergence Analysiscited by 10
  12. 2024Fast-Convergent and Communication-Alleviated Heterogeneous Hierarchical Federated Learning in Autonomous Drivingcited by 8
35 more
  1. 2024Achieving Linear Speedup in Asynchronous Federated Learning with Heterogeneous Clientscited by 7
  2. 2024Hierarchical Federated Learning with Multi-Timescale Gradient Correctioncited by 7
  3. 2022Hierarchical Federated Learning with Momentum Acceleration in Multi-Tier Networkscited by 6
  4. 2024Hierarchical Over-the-Air Federated Learning with Awareness of Interference and Data Heterogeneitycited by 6
  5. 2024The Effect of Quantization in Federated Learning: A R'enyi Differential Privacy Perspectivecited by 6
  6. 2024FedDM: Enhancing Communication Efficiency and Handling Data Heterogeneity in Federated Diffusion Modelscited by 5
  7. 2024Hierarchical Federated ADMMcited by 4
  8. 2023Federated Learning: A Cutting-Edge Survey of the Latest Advancements and Applicationscited by 3
  9. 2025Age-Based Device Selection and Transmit Power Optimization in Over-the-Air Federated Learningcited by 3
  10. 2025Research in Collaborative Learning Does Not Serve Cross-Silo Federated Learning in Practicecited by 3
  11. 2023FedNC: A Secure and Efficient Federated Learning Method with Network Codingcited by 2
  12. 2023Binary Federated Learning with Client-Level Differential Privacycited by 2
  13. 2024Collaborative Visual Place Recognition through Federated Learningcited by 2
  14. 2025Communication-Efficient and Personalized Federated Foundation Model Fine-Tuning via Tri-Matrix Adaptationcited by 2
  15. 2025FedHQ: Hybrid Runtime Quantization for Federated Learningcited by 2
  16. 2023Federated Learning over Hierarchical Wireless Networks: Training Latency Minimization via Submodel Partitioningcited by 1
  17. 2024A Federated Online Restless Bandit Framework for Cooperative Resource Allocationcited by 1
  18. 2024Sequential Federated Learning in Hierarchical Architecture on Non-IID Datasetscited by 1
  19. 2024Federated Low-Rank Adaptation with Differential Privacy over Wireless Networkscited by 1
  20. 2025Beyond Model Scale Limits: End-Edge-Cloud Federated Learning with Self-Rectified Knowledge Agglomerationcited by 1
  21. 2025A Generalized Hierarchical Federated Learning Framework with Theoretical Guaranteescited by 1
  22. 2026Age-Aware Edge-Blind Federated Learning via Over-the-Air Aggregationcited by 1
  23. 2026Decentralized Federated Learning With Energy Harvesting Devicescited by 1
  24. 2026EdgeFLow: Serverless Federated Learning via Sequential Model Migration in Edge Networkscited by 1
  25. 2023Client Orchestration and Cost-Efficient Joint Optimization for NOMA-Enabled Hierarchical Federated Learningcited by 0
  26. 2024A Hierarchical Federated Learning Approach for the Internet of Thingscited by 0
  27. 2024Personalized Multi-tier Federated Learningcited by 0
  28. 2024Twin Sorting Dynamic Programming Assisted User Association and Wireless Bandwidth Allocation for Hierarchical Federated Learningcited by 0
  29. 2025Smoothing ADMM for Non-convex and Non-smooth Hierarchical Federated Learningcited by 0
  30. 2025Free Privacy Protection for Wireless Federated Learning: Enjoy It or Suffer from It?cited by 0
  31. 2026Mitigating Heterogeneity-Induced Drift in Hierarchical Sign-Based Federated Learningcited by 0
  32. 2026Federated Multi Agent Deep Learning and Neural Networks for Advanced Distributed Sensing in Wireless Networkscited by 0
  33. 2026Hierarchical Federated Learning for Networked AI: From Communication Saving to Architecture-Aware Designcited by 0
  34. 2026Towards Serverless Semi-Decentralized Federated Learning with Heterogeneous Optimizerscited by 0
  35. 2026SpeechLLM Meets Federated Learning for End-to-End ASR: English and Italian Case Studiescited by 0