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Energy-Efficient Wireless Federated Learning via Doubly Adaptive Quantization

Xuefeng Han, Wen Chen, Jun Li, Ming Ding, Qingqing Wu, Kang Wei, Xiumei Deng, Zhen Mei

TL;DR

This work tackles energy-efficient wireless federated learning by introducing a doubly adaptive quantization (quantization levels that rise with training and adapt to client data sizes) and a joint resource design (QCCF) that includes client scheduling, channel allocation, and computation frequency control. Using Lyapunov optimization, the authors transform the long-term energy minimization into per-round problems, solved via a convex per-client subproblem (with a closed-form KKT solution) and a genetic algorithm for channel allocation. Theoretical results provide an upper bound on FL convergence incorporating quantization error and data heterogeneity, guiding the per-round decisions. Experiments on FEMNIST and CIFAR-10 demonstrate substantial energy savings and faster convergence compared to baselines, with quantization behavior aligning with the proposed theoretical insights.

Abstract

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.

Energy-Efficient Wireless Federated Learning via Doubly Adaptive Quantization

TL;DR

This work tackles energy-efficient wireless federated learning by introducing a doubly adaptive quantization (quantization levels that rise with training and adapt to client data sizes) and a joint resource design (QCCF) that includes client scheduling, channel allocation, and computation frequency control. Using Lyapunov optimization, the authors transform the long-term energy minimization into per-round problems, solved via a convex per-client subproblem (with a closed-form KKT solution) and a genetic algorithm for channel allocation. Theoretical results provide an upper bound on FL convergence incorporating quantization error and data heterogeneity, guiding the per-round decisions. Experiments on FEMNIST and CIFAR-10 demonstrate substantial energy savings and faster convergence compared to baselines, with quantization behavior aligning with the proposed theoretical insights.

Abstract

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.
Paper Structure (31 sections, 6 theorems, 55 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 31 sections, 6 theorems, 55 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. Federated Learning with Model Quantization
  5. Federated Learning Process
  6. Decision
  7. Broadcasting
  8. Local updating and Quantization
  9. Uploading
  10. Global aggregation
  11. Quantization Method
  12. Convergence Analysis
  13. Assumptions and Definitions
  14. Results
  15. Problem Formulation
  16. ...and 16 more sections

Key Result

Lemma 1

For the quantization function $Q(\cdot)$, the accurate local model is unbiasedly estimated by $\mathbb E[Q(\bm \theta^{n, \tau}_i)] = \bm \theta^{n, \tau}_i,$ and the variance is bounded by $\mathbb E\left[ \left\|Q(\bm \theta^{n, \tau}_i) - \bm \theta^{n, \tau}_i \right\|^2 \right] \leq \frac{Z (\t

Figures (5)

  • Figure 1: There are 5 steps in each communication round of our FL framework.
  • Figure 2: Test accuracy and accumulated energy consumption curves of the QCCF algorithm with different V values.
  • Figure 3: Test accuracy curves and accumulated energy consumption curves of related algorithms on the FEMNIST dataset.
  • Figure 4: Test accuracy curves and accumulated energy consumption curves of related algorithms on the CIFAR-10 dataset.
  • Figure 5: The relationships of quantization levels with the training process and dataset sizes for related algorithms.

Theorems & Definitions (7)

  • Lemma 1
  • Definition 1
  • Lemma 2
  • Theorem 1
  • Theorem 2
  • Lemma 3
  • Theorem 3