# Hierarchical Federated Learning in Wireless Networks: Pruning Tackles Bandwidth Scarcity and System Heterogeneity

arXiv: https://arxiv.org/abs/2308.01562 · HTML: https://mlsanity.com/paper/2308.01562/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 37 references that are in the map.
- First posted on arXiv 3 Aug 2023.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [Model Pruning Enables Efficient Federated Learning on Edge Devices](https://mlsanity.com/paper/1909.12326/) (2019)
- [Client-Edge-Cloud Hierarchical Federated Learning](https://mlsanity.com/paper/1905.06641/) (2019)
- [Energy Efficient Federated Learning Over Wireless Communication Networks](https://mlsanity.com/paper/1911.02417/) (2019)
- [Dynamic Model Pruning with Feedback](https://mlsanity.com/paper/2006.07253/) (2020)
- [Hierarchical Federated Learning Across Heterogeneous Cellular Networks](https://mlsanity.com/paper/1909.02362/) (2019)
- [HFEL: Joint Edge Association and Resource Allocation for Cost-Efficient Hierarchical Federated Edge Learning](https://mlsanity.com/paper/2002.11343/) (2020)
- [Multi-Stage Hybrid Federated Learning over Large-Scale D2D-Enabled Fog Networks](https://mlsanity.com/paper/2007.09511/) (2020)
- [Anarchic Federated Learning](https://mlsanity.com/paper/2108.09875/) (2021)
- [Mobility-Aware Cluster Federated Learning in Hierarchical Wireless Networks](https://mlsanity.com/paper/2108.09103/) (2021)
- [Demystifying Why Local Aggregation Helps: Convergence Analysis of Hierarchical SGD](https://mlsanity.com/paper/2010.12998/) (2020)
- [Resource Constrained Vehicular Edge Federated Learning with Highly Mobile Connected Vehicles](https://mlsanity.com/paper/2210.15496/) (2022)
- [Optimal 3D-Trajectory Design and Resource Allocation for Solar-Powered UAV Communication Systems](https://mlsanity.com/paper/1808.00101/) (2018)
- [Communication Efficient Federated Learning with Energy Awareness over Wireless Networks](https://mlsanity.com/paper/2004.07351/) (2020)
- [FedLP: Layer-wise Pruning Mechanism for Communication-Computation Efficient Federated Learning](https://mlsanity.com/paper/2303.06360/) (2023)
- [Towards Communication-Learning Trade-off for Federated Learning at the Network Edge](https://mlsanity.com/paper/2205.14271/) (2022)

## Built on by (most cited first, 10 of 10)

- [Resource-Aware Hierarchical Federated Learning in Wireless Video Caching Networks](https://mlsanity.com/paper/2402.04216/) (2024)
- [Hierarchical Federated ADMM](https://mlsanity.com/paper/2409.18796/) (2024)
- [Federated Learning over Hierarchical Wireless Networks: Training Latency Minimization via Submodel Partitioning](https://mlsanity.com/paper/2310.17890/) (2023)
- [Resource-Aware Hierarchical Federated Learning for Video Caching in Wireless Networks](https://mlsanity.com/paper/2311.06918/) (2023)
- [Online-Score-Aided Federated Learning for Resource-Constrained Wireless Clients with Continual Data Arrival](https://mlsanity.com/paper/2408.05886/) (2024)
- [Reactive Orchestration for Hierarchical Federated Learning Under a Communication Cost Budget](https://mlsanity.com/paper/2412.03385/) (2024)
- [A Hierarchical Federated Learning Approach for the Internet of Things](https://mlsanity.com/paper/2403.01540/) (2024)
- [Personalized Hierarchical Split Federated Learning in Wireless Networks](https://mlsanity.com/paper/2411.06042/) (2024)
- [Computation- and Communication-Efficient Online FL for Resource-Constrained Aerial Vehicles](https://mlsanity.com/paper/2506.02972/) (2025)
- [From Privacy to Trust in the Agentic Era: A Taxonomy of Challenges in Trustworthy Federated Learning Through the Lens of Trust Report 2.0](https://mlsanity.com/paper/2507.15796/) (2025)

## Abstract (arXiv)

While a practical wireless network has many tiers where end users do not directly communicate with the central server, the users' devices have limited computation and battery powers, and the serving base station (BS) has a fixed bandwidth. Owing to these practical constraints and system models, this paper leverages model pruning and proposes a pruning-enabled hierarchical federated learning (PHFL) in heterogeneous networks (HetNets). We first derive an upper bound of the convergence rate that clearly demonstrates the impact of the model pruning and wireless communications between the clients and the associated BS. Then we jointly optimize the model pruning ratio, central processing unit (CPU) frequency and transmission power of the clients in order to minimize the controllable terms of the convergence bound under strict delay and energy constraints. However, since the original problem is not convex, we perform successive convex approximation (SCA) and jointly optimize the parameters for the relaxed convex problem. Through extensive simulation, we validate the effectiveness of our proposed PHFL algorithm in terms of test accuracy, wall clock time, energy consumption and bandwidth requirement.