Title Page
Abstract
Contents
Chapter 1. Introduction 14
1.1. Federated Learning 14
1.2. Over-the-Air Computation 21
1.3. Over-the-Air Federated Learning 28
Chapter 2. Device Selection for Over-the-Air Federated Learning 31
2.1. Over-the-Air FL System with Device Selection 32
2.1.1. System Model 32
2.1.2. Aggregation Noise in AirComp 35
2.1.3. Problem Formulation 38
2.2. Analysis of FL System with Device Selection 39
2.2.1. Device Selection with Random Beamforming 39
2.2.2. Convergence of FL with Device Selection 41
2.3. Sparse Optimization for Device Selection in FL 43
2.3.1. ℓ₁-Norm Minimization Problem 43
2.3.2. KKT Conditions 46
2.4. Beamforming Vector Design 48
2.4.1. Convex Subproblems based on MM Approach 48
2.4.2. Low-Complexity Algorithm 50
2.4.3. Discussion of How Optimization Algorithm Works 53
2.5. Numerical Results 55
2.6. Summary 66
Chapter 3. Device Selection in IRS-aided Over-the-Air FL 68
3.1. Over-the-Air FL System with IRS 69
3.1.1. System Model 69
3.2. Alternating Optimization of Beamforming Vector and Phase Shift 72
3.2.1. Optimizing Beamforming Vector 73
3.2.2. Optimizing Phase Shifts 74
3.3. Numerical Results 79
3.4. Summary 84
Chapter 4. Joint Beamforming Vector Design and Learning Rate Optimization 85
4.1. Over-the-Air FL System with Dynamic Learning Rate 86
4.1.1. System Model 86
4.1.2. Problem Formulation 89
4.2. Effect of Multiple Antennas on Aggregation 91
4.3. Joint Design of Beamforming Vector and Dynamic Learning Rate 95
4.3.1. Convex Subproblems based on MM Approach 95
4.3.2. Low-Complexity Algorithm 96
4.4. Numerical Results 99
4.5. Summary 104
Chapter 5. Conclusions 105
Appendix 107
A. Proof of Theorem 2.1 107
B. Proof of Theorem 2.2 112
C. Proof of Theorem 2.3 113
D. Proof of Theorem 2.4 114
E. Proof of Theorem 4.1 115
Bibliography 116
초록 124
Table 1.1. Example of nomographic functions. 24
Table 2.1. Learning performance for different datasets and ML model. 64
Table 2.2. Runtime of different device selection algorithms. 65
Table 3.1. Prediction accuracy at the 100-th communication round. 83
Table 3.2. Runtime of different device selection algorithms. 84
Table 4.1. Prediction accuracy of benchmarks with dynamic learning rate for different ML configurations. 104
Figure 1.1. A type of distributed learning. 18
Figure 1.2. System model of centralized/federated learning. 19
Figure 1.3. Multiple access channel with K UEs. 22
Figure 1.4. Conventional approach versus AirComp via MAC 23
Figure 1.5. System model of over-the-air computation 25
Figure 1.6. System model of AirComp FL. 29
Figure 2.1. System model of over-the-air FL with device selection. 33
Figure 2.2. Illustration of how the proposed algorithm works. 53
Figure 2.3. The average number of selected devices S with respect to the MSE requirement γ. 57
Figure 2.4. The average number of selected devices S with respect to the total number of devices K (γ = 4). 57
Figure 2.5. Relation between the MSE requirement γ and the scaled MSE upper-bound P/σ²δ = γE[1/S²].[이미지참조] 59
Figure 2.6. Prediction accuracy with respect to MSE requirement γ for different SNR. 60
Figure 2.7. Prediction accuracy for the imbalanced channel between local devices and BS and different data distributions (SNR = -24 dB). 60
Figure 2.8. Prediction accuracy with respect to the communication rounds (γ = 4 dB). 63
Figure 3.1. System model of the IRS-aided AirComp FL 70
Figure 3.2. Simulation configuration for the IRS-aided FL. 80
Figure 3.3. The number of selected devices S with respect to the MSE requirement γ (M = 60, K = 100). 81
Figure 3.4. The number of selected devices S with respect to the total number of devices K (M = 60, γ = 20 dB). 82
Figure 3.5. Prediction accuracy with respect to the number of communication rounds 82
Figure 4.1. System model of over-the-air FL with dynamic learning rate. 87
Figure 4.2. The MSE versus the number of iterations. 100
Figure 4.3. The MSE versus the total number of devices K (N = 16). 101
Figure 4.4. The MSE with respect to the communication rounds (N = 16, K = 60, M = 2). 102
Figure 4.5. Prediction accuracy with respect to the communication rounds (N = 16, K = 60, M = 2, P/σ² = -10 dB). 103