Energy-Efficient Wireless Federated Learning via Doubly Adaptive Quantization

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.