Federated learning (FL) has been recognized as a viable distributed learning paradigm for training a machine learning model across distributed clients without uploading raw data. However, FL in wireless networks still faces two major challenges, i.e., large communication overhead and high energy consumption, which are exacerbated by client heterogeneity in dataset sizes and wireless channels. While model quantization is effective for energy reduction, existing works ignore adapting quantization to heterogeneous clients and FL convergence. To address these challenges, this paper develops an energy optimization problem of jointly designing quantization levels, scheduling clients, allocating channels, and controlling computation frequencies (QCCF) in wireless FL. Specifically, we derive an upper bound identifying the influence of client scheduling and quantization errors on FL convergence. Under the longterm convergence constraints and wireless constraints, the problem is established and transformed into an instantaneous problem with Lyapunov optimization. Solving Karush-Kuhn-Tucker conditions, our closed-form solution indicates that the doubly adaptive quantization level rises with the training process and correlates negatively with dataset sizes. Experiment results validate our theoretical results, showing that QCCF consumes less energy with faster convergence compared with state-of-the-art baselines.

翻译：联邦学习已被视为一种无需上传原始数据、在分布式客户端间训练机器学习模型的有效分布式学习范式。然而，无线网络中的联邦学习仍面临两大主要挑战：通信开销大和能耗高，而客户端数据集大小与无线信道的异构性进一步加剧了这些问题。尽管模型量化能有效降低能耗，但现有工作忽略了量化对异构客户端及联邦学习收敛性的自适应调整。为解决这些挑战，本文提出了一个联合设计量化等级、客户端调度、信道分配及计算频率的无线联邦学习能效优化问题。具体而言，我们推导了客户端调度与量化误差对联邦学习收敛性影响的上界，并在长期收敛约束与无线资源约束下建立该问题，利用Lyapunov优化将其转化为瞬时问题。通过求解Karush-Kuhn-Tucker条件，我们得到的闭式解表明：双重自适应量化等级随训练过程递增，并与数据集大小呈负相关。实验结果验证了理论分析，显示相比现有最优基准方法，所提方法在加快收敛速度的同时能耗更低。