Hierarchical Federated Learning (HFL) has emerged as a promising approach for scalable and communication-efficient model training in wireless networks. However, achieving energy efficiency while ensuring convergence remains challenging due to limited bandwidth resource and strict latency constraints. This paper addresses energy-efficient HFL under both statistical and system heterogeneity, aiming to minimize long-term energy consumption through adaptive and unbiased edge scheduling and resource allocation in dynamic environments. A convergence analysis is first conducted without relying on a convex assumption, explicitly characterizing the influences of the number of scheduled edges and scheduling probabilities. An iterative algorithm is then proposed to jointly optimize these variables: the scheduling probabilities are solved by using a Barrier Method (BM) with an Infeasible-Start Newton Method (ISNM), while the number of scheduled edges is derived in a closed form. To further enhance communication efficiency, Non-Orthogonal Multiple Access (NOMA) is employed at the user–edge layer. Then, a joint optimization of inter-edge bandwidth allocation and intra-edge local resource allocation is developed to balance computation and communication overhead. Extensive simulations demonstrate that the proposed framework significantly outperforms existing benchmarks in terms of energy consumption under Non-Independent and Identically Distributed (Non-IID) data and dynamic wireless environments.

Hierarchical Federated Learning (HFL) has been proposed to achieve large-scale model training and more efficient communication, surpassing conventional Federated Learning (FL). However, inappropriate aggregation frequency and edge association in HFL result in excessive energy consumption for users with poor channels or hinder its convergence performance due to stochastic gradient descent (SGD) and Non-Independent and Identical Distribution (NIID) data, which is particularly challenging for energy-limited users. Motivated by this, a joint aggregation frequency and edge association optimization problem is proposed to minimize the long-term energy consumption during HFL training process. The problem can be formulated by incorporating computation, communication model and convergence analysis together. Due to the coupling between control variables, we decompose it into two sub-problems and adopt an iterative algorithm to approximate their optimal solutions. Specifically, the aggregation frequency is optimized under a given edge association by convex optimization to trade-off the computation and communication energy consumption, considering the convergence characteristic and SGD noise. Then, Deep Reinforcement Learning (DRL) is adopted to optimize edge association based on data distribution, dynamic channels and the derived aggregation frequency. Simulation results demonstrate that our proposed strategy achieves the lowest energy consumption while attaining the required model accuracy, outperforming other benchmarks.

Hierarchical Federated Learning (HFL) has been introduced to enhance the communication efficiency and scalability of traditional Federated Learning (FL). In addition, the integration of Non-Orthogonal Multiple Access (NOMA) into the HFL framework serves to bolster system capacity and spectral efficiency. However, the formidable challenge of energy efficiency persists, particularly in energy-constrained scenarios, which can be further compounded by factors such as Non-Independent and Identical Distribution (NIID) data, varying channels across users, heterogeneous computation and communication resources, and the interference from weak users. Motivated by this, we aim to minimize the sum of the computation and communication energy consumption of all users in the NOMA-based HFL system. This is achieved through a joint optimization of User-Edge Association (UEA) and Resource Allocation (RA). Specifically, we utilize Deep Reinforcement Learning (DRL) to optimize UEA to achieve the objective from a long-term perspective. Subsequently, computation and communication resources are jointly optimized by Newton's Method to balance the computation and communication energy consumption while meeting a given latency requirement. Numerical results show that our strategy significantly improves energy efficiency of the system compared with other benchmarks.

Hierarchical Federated Learning (HFL) has been proposed to achieve larger-scale model training and more efficient communications compared to conventional Federated Learning (FL). However, both inappropriate edge association strategy and aggregation frequency may consume massive energy in users with poor channel conditions or degrade the HFL convergence performance due to Non Independent and Identical Distribution (NIID) data, which is challenging to energy-limited users. Motivated by this, a dynamically joint edge association and aggregation frequency optimization problem is proposed from the perspective of minimizing long-term energy consumption. By incorporating the communication model and convergence analysis, the problem can be formulated to strike a balance between HFL convergence rate and energy consumed by all users within one global communication round. Then, a Deep Reinforcement Learning (DRL) agent is designed to approximate the optimal solution. Simulation results verify the convergence analysis and the proposed DRL-assisted joint strategy can consume the least energy while reaching the required target model accuracy compared to other benchmarks.

Federated Learning (FL) is widely regarded as a leading distributed machine learning paradigm, owing to its outstanding performance in preserving privacy and conserving communication resources. To use it efficiently in wireless communication networks, novel transmission schemes that jointly consider the model propagation and training features are required. In this paper, a novel joint user scheduling and resource allocation scheme is proposed to reduce the communication cost in terms of the weighted sum of energy and time consumption while ensuring the convergence of FL. The time-varying channels and unpredictable model loss in the system make it difficult to use conventional optimization methods for this problem. Furthermore, considering optimal transmission policy in FL is to train a qualified model in the dynamic iterative process, a deep reinforcement learning based Proximal Policy Optimization (PPO) approach is employed to train an automatic policy maker. Specifically, the dynamic policy is decided in each training round based on the observed model accuracy and the time-varying channel gains, aiming at minimizing the total cost. Simulation results verify the proposed scheme can reduce the defined communication cost and improve the training efficiency compared with the traditional greedy and random benchmarks.