mlsanityData to 14 Oct 2026

Demystifying Why Local Aggregation Helps: Convergence Analysis of Hierarchical SGD

arXiv 2010.12998 ↗First posted 24 Oct 2020cs.LG cs.DC cs.ITcited by 26

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Abstract (arXiv)

Hierarchical SGD (H-SGD) has emerged as a new distributed SGD algorithm for multi-level communication networks. In H-SGD, before each global aggregation, workers send their updated local models to local servers for aggregations. Despite recent research efforts, the effect of local aggregation on global convergence still lacks theoretical understanding. In this work, we first introduce a new notion of "upward" and "downward" divergences. We then use it to conduct a novel analysis to obtain a worst-case convergence upper bound for two-level H-SGD with non-IID data, non-convex objective function, and stochastic gradient. By extending this result to the case with random grouping, we observe that this convergence upper bound of H-SGD is between the upper bounds of two single-level local SGD settings, with the number of local iterations equal to the local and global update periods in H-SGD, respectively. We refer to this as the "sandwich behavior". Furthermore, we extend our analytical approach based on "upward" and "downward" divergences to study the convergence for the general case of H-SGD with more than two levels, where the "sandwich behavior" still holds. Our theoretical results provide key insights of why local aggregation can be beneficial in improving the convergence of H-SGD.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). First posted on arXiv 24 Oct 2020.

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Citing papers per year: 2021: 2; 2022: 5; 2023: 8; 2024: 10; 2025: 0; 2026: 1.

26 papers.

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  2. 2022Scalable and Low-Latency Federated Learning with Cooperative Mobile Edge Networkingcited by 18
  3. 2024Mobility Accelerates Learning: Convergence Analysis on Hierarchical Federated Learning in Vehicular Networkscited by 11
  4. 2022Multi-Edge Server-Assisted Dynamic Federated Learning with an Optimized Floating Aggregation Pointcited by 10
  5. 2023Adaptive Federated Pruning in Hierarchical Wireless Networkscited by 10
  6. 2023Hierarchical Federated Learning in Wireless Networks: Pruning Tackles Bandwidth Scarcity and System Heterogeneitycited by 10
  7. 2024Satellite Federated Edge Learning: Architecture Design and Convergence Analysiscited by 10
  8. 2023Delay Sensitive Hierarchical Federated Learning with Stochastic Local Updatescited by 8
  9. 2022Confederated Learning: Federated Learning with Decentralized Edge Serverscited by 7
  10. 2023Flame: Simplifying Topology Extension in Federated Learningcited by 7
  11. 2024Hierarchical Federated Learning with Multi-Timescale Gradient Correctioncited by 7
  12. 2021FedFog: Network-Aware Optimization of Federated Learning over Wireless Fog-Cloud Systemscited by 6
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  2. 2023Data-Aware Gradient Compression for FL in Communication-Constrained Mobile Computingcited by 5
  3. 2024Resource-Aware Hierarchical Federated Learning in Wireless Video Caching Networkscited by 4
  4. 2024Communication-Efficient Adaptive Batch Size Strategies for Distributed Local Gradient Methodscited by 4
  5. 2023WW-FL: Secure and Private Large-Scale Federated Learningcited by 2
  6. 2024UAV-assisted Unbiased Hierarchical Federated Learning: Performance and Convergence Analysiscited by 2
  7. 2022Hierarchical Over-the-Air FedGradNormcited by 1
  8. 2023Federated Learning over Hierarchical Wireless Networks: Training Latency Minimization via Submodel Partitioningcited by 1
  9. 2023Resource-Aware Hierarchical Federated Learning for Video Caching in Wireless Networkscited by 1
  10. 2024A Hierarchical Federated Learning Approach for the Internet of Thingscited by 0
  11. 2024Personalized Multi-tier Federated Learningcited by 0
  12. 2024Heterogeneity-Aware Resource Allocation and Topology Design for Hierarchical Federated Edge Learningcited by 0
  13. 2024Personalized Hierarchical Split Federated Learning in Wireless Networkscited by 0
  14. 2026Fed-BAC: Federated Bandit-Guided Additive Clustering in Hierarchical Federated Learningcited by 0