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Joint Energy and Latency Optimization in Federated Learning over Cell-Free Massive MIMO Networks

Afsaneh Mahmoudi, Mahmoud Zaher, Emil Björnson

TL;DR

This work tackles energy and latency efficiency in FL over CFmMIMO by jointly optimizing uplink transmit powers. It formulates a weighted objective $\nu(\bp)=\sum_{j=1}^K \theta_1 E_j + \theta_2 \ell_j$ and shows a unique minimum for each $p_j$, enabling a fast coordinate gradient descent algorithm to jointly minimize uplink energy and training latency under power constraints $0 \le p_j \le 1$. The authors derive closed-form derivative expressions and use them in an iterative scheme to compute the optimal powers, then determine $T_{\max}$ based on energy and latency budgets. Numerical results on a CFmMIMO testbed with $M=16$ APs and $K\in\{20,40\}$ (CIFAR-10) show substantial gains over max-sum rate and Dinkelbach baselines, illustrating the practical impact for energy-aware, latency-constrained FL in wireless networks.

Abstract

Federated learning (FL) is a distributed learning paradigm wherein users exchange FL models with a server instead of raw datasets, thereby preserving data privacy and reducing communication overhead. However, the increased number of FL users may hinder completing large-scale FL over wireless networks due to high imposed latency. Cell-free massive multiple-input multiple-output~(CFmMIMO) is a promising architecture for implementing FL because it serves many users on the same time/frequency resources. While CFmMIMO enhances energy efficiency through spatial multiplexing and collaborative beamforming, it remains crucial to meticulously allocate uplink transmission powers to the FL users. In this paper, we propose an uplink power allocation scheme in FL over CFmMIMO by considering the effect of each user's power on the energy and latency of other users to jointly minimize the users' uplink energy and the latency of FL training. The proposed solution algorithm is based on the coordinate gradient descent method. Numerical results show that our proposed method outperforms the well-known max-sum rate by increasing up to~$27$\% and max-min energy efficiency of the Dinkelbach method by increasing up to~$21$\% in terms of test accuracy while having limited uplink energy and latency budget for FL over CFmMIMO.

Joint Energy and Latency Optimization in Federated Learning over Cell-Free Massive MIMO Networks

TL;DR

This work tackles energy and latency efficiency in FL over CFmMIMO by jointly optimizing uplink transmit powers. It formulates a weighted objective and shows a unique minimum for each , enabling a fast coordinate gradient descent algorithm to jointly minimize uplink energy and training latency under power constraints . The authors derive closed-form derivative expressions and use them in an iterative scheme to compute the optimal powers, then determine based on energy and latency budgets. Numerical results on a CFmMIMO testbed with APs and (CIFAR-10) show substantial gains over max-sum rate and Dinkelbach baselines, illustrating the practical impact for energy-aware, latency-constrained FL in wireless networks.

Abstract

Federated learning (FL) is a distributed learning paradigm wherein users exchange FL models with a server instead of raw datasets, thereby preserving data privacy and reducing communication overhead. However, the increased number of FL users may hinder completing large-scale FL over wireless networks due to high imposed latency. Cell-free massive multiple-input multiple-output~(CFmMIMO) is a promising architecture for implementing FL because it serves many users on the same time/frequency resources. While CFmMIMO enhances energy efficiency through spatial multiplexing and collaborative beamforming, it remains crucial to meticulously allocate uplink transmission powers to the FL users. In this paper, we propose an uplink power allocation scheme in FL over CFmMIMO by considering the effect of each user's power on the energy and latency of other users to jointly minimize the users' uplink energy and the latency of FL training. The proposed solution algorithm is based on the coordinate gradient descent method. Numerical results show that our proposed method outperforms the well-known max-sum rate by increasing up to~\% and max-min energy efficiency of the Dinkelbach method by increasing up to~\% in terms of test accuracy while having limited uplink energy and latency budget for FL over CFmMIMO.
Paper Structure (11 sections, 2 theorems, 23 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 11 sections, 2 theorems, 23 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Federated Averaging
  4. Uplink Process in CFmMIMO
  5. Channel Estimation
  6. Uplink Data Transmission
  7. Problem Formulation
  8. Solution Algorithm
  9. Numerical Results
  10. Conclusion and Future work
  11. Proof of Lemma \ref{['lemma: J_cnx']}

Key Result

Lemma 1

Let $E_j$ and $\ell_j$ be the energy and latency for sending each local FL model $\bw_t^j$ to the APs. We define ${\nu}(\bp;\theta_1,\theta_2, b, d):= \sum_{j=1}^K \theta_1~E_j~+~\theta_2~\ell_j$ as the objective function in optimization1. When all other variables are fixed, ${\nu}(\bp;\theta_1, \th

Figures (4)

  • Figure 1: General architecture of FL over CFmMIMO.
  • Figure 2: Performance of our approach for different $\theta_1$ and $\theta_2$, $K =20$.
  • Figure 3: Antenna implementation cost.
  • Figure 4: FL test accuracy.

Theorems & Definitions (2)

  • Lemma 1
  • Proposition 1