Joint communication-learning design for over-the-air federated learning = 무선 연합 학습을 위한 통신 및 학습의 공동 최적화|RISS 상세보기

국문 초록 (Abstract)

최근 무선 통신 기술의 발전으로 광범위한 사물 인터넷 장치로부터 정보를 수집하며 데이터 기반 접근 방식의 발전을 이끌고 있다. 분산되어 있는 로컬 장치로부터 획득된 로컬 데이터로 기계 학습 모델을 훈련하기 위해서 일반적으로 고성능 클라우드 서버가 전체 데이터 처리하는 중앙 집중식 방식을 주로 채택하고 있다. 하지만 로컬 장치에서 클라우드 서버로 데이터를 전송하는 것은 개인 정보 보호, 제한된 무선 자원 등의 문제로 바람직하지 않거나 구현하는 것이 불가능하다. 최근 연합 학습(federated learning)이라는 분산형 방식이 글로벌 모델을 중앙 집중식 방식의 문제를 해결함으로써 주목받고 있다. 연합 학습은 로컬 장치로부터의 직접적인 데이터 전송 없이 기계 학습 모델을 학습할 수 있으므로 중앙 집중식 방식의 문제를 완화하였다. 하지만 차세대 통신에서는 더 많은 로컬 장치가 통신하기를 바라며 기계 학습에서는 학습을 위한 더 많은 로컬 데이터를 바라기 때문에 연합 학습을 가능하게 하는 새로운 무선 시스템을 설계하는 것이 중요하다.
무선 연산(over-the-air computation)은 다중 접속 채널에서 신호 중첩의 원리를 이용하여 각 로컬 디바이스로부터 송신된 신호들이 집계된 정보를 획득하며 기지국과 로컬 장치 간의 통신 오버헤드를 줄일 수 있다. 연합 학습에서 클라우드 서버는 개별 로컬 장치의 모델 정보가 필요하지 않으며 로컬 모델들이 집계된 정보만 필요하다. 따라서 무선 연합 학습(over-the-air federated learning)은 더 많은 장치가 학습에 참여하는 것을 가능하게 하며 인공지능을 위한 차세대 통신으로 주목받고 있다. 그러나 이러한 이점에도 불구하고 무선 연합 학습은 제한된 자원, 신뢰성, 데이터 이질성 등과 같은 몇 가지 문제가 존재한다. 본 논문에서는 무선연합 학습에서의 기계 학습 모델의 안정성 및 학습 성능에 대해서 논의한다.
본 논문에서는 먼저 무선 연합 학습에서의 빔포밍 벡터 설계 및 장치 선택 알고리즘을 제안한다. 일반적으로 학습에 참여하는 장치가 많을수록 인공지능 모델의 성능이 향상되는 것이 잘 알려져 있다. 하지만 더 많은 장치가 학습에 참여하기 위해서는 무선 연합 학습에서 학습 성능을 저하할 수 있는 집계 에러가 커야 한다는 문제가 있다. 따라서 본 논문에서는 제한된 집계 에러 내에서 연합 학습에 참여하는 장치의 수를 최대화하는 문제를 해결한다. 다음으로 연합 학습에 참여하는 장치를 선택하기 위해 차세대 통신의 해결책으로 주목받고 있는 메타물질 기반의 지능형 반사 표면(Intelligent Reflecting Surface)과 빔포밍 벡터를 동시에 최적화하는 알고리즘을 제안한다. 마지막으로 기계 학습에서의 중요한 요소인 학습률(learning rate)과 빔포밍 벡터를 동시에 설계하여 무선 연합 학습에서의 집계 에러를 줄이고 안정적인 학습 성능을 달성하게 하는 알고리즘을 제안한다.

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최근 무선 통신 기술의 발전으로 광범위한 사물 인터넷 장치로부터 정보를 수집하며 데이터 기반 접근 방식의 발전을 이끌고 있다. 분산되어 있는 로컬 장치로부터 획득된 로컬 데이터로 기...

다국어 초록 (Multilingual Abstract)

Advances in wireless communication technologies simplify the process of collecting data from a wide range of IoT devices. This data from IoT devices can be used to increase the effectiveness of a data-driven approach. Training artificial intelligence models on extensive datasets acquired from distributed local devices generally employs a centralized approach, where a high-performance cloud server handles the entire dataset. However, transmitting data from devices to a cloud server is undesirable or infeasible due to privacy issues and the limitations of wireless resources. In addition, 6G networks are expected to accommodate 107 devices. Federated learning (FL) is emerging as an approach to mitigate the problems of a centralized approach, allowing devices to obtain updated machine learning (ML) models without transmitting local data. However, it is critical to design a new wireless system that enables FL due to the high communication costs associated with inherently high-dimensional model parameters and many participating local devices.
AirComp is emerging as an effective strategy to eliminate the communication overhead between the base station and the devices to overcome this drawback. In the context of FL, it’s important to note that the cloud server solely relies on aggregated local models and doesn’t require access to individual information from local devices. As a result, the wireless resource requirement can remain decoupled from the number of devices, as the aggregation of local model information is achieved over wireless networks. AirComp uses the waveform superposition property of a MAC to obtain aggregated signals. It increases the efficiency of wireless communications by aggregating the trans- mitted local model parameters from local devices at the same time over the air. As a result, over-the-air FL for ML is being envisioned for 6G networks. Despite its potential benefits, over-the-air FL presents several technical and practical challenges, such as limited resources, data heterogeneity, and reliability. In this dissertation, our focus is mainly on the improvement of the ML performance and robustness in over-the-air FL.
In the first part of this dissertation, we consider a new device selection algorithm with a beamforming vector design for over-the-air FL. It is well known that including more devices in the FL generally improves learning performance. However, aggregation errors increase when many devices participate in FL. This can result in poor learning performance. Therefore, we formulate an AirComp beamforming problem to maximize the number of selected devices with a given MSE threshold. We also show that the AirComp problem in the uplink is the same as the multicast problem in the downlink. Numerical results show that the proposed low-complexity scheme is faster and more powerful than existing algorithms based on semidefinite relaxation (SDR). In addition, the learning performance is improved by selecting only a subset of devices to reduce the MSE between the post-processed signal and the FedAvg output.
In the second part of this dissertation, we provide a joint design algorithm of the phase shifts and the beamforming vector in over-the-air FL with an intelligent reflecting surface (IRS). Learning performance improves as more devices participate in the FL, and the IRS allows more devices to transmit simultaneously. Therefore, a more compact problem is presented that is equivalent to a conventional design problem for beamforming vector and phase shifts. This problem is formulated as a mixed combinatorial optimization problem with non-convex constraints. In order to handle its non-convexity, we apply an alternating optimization (AO) and majorization minimization (MM) approach. We propose a new joint optimization algorithm and prove that its solution converges to Karush-Kuhn-Tucker (KKT) points.
In the third part of this dissertation, we provide a joint optimization algorithm for the beamforming vector and the dynamic learning rate. In ML, the learning rate is an important parameter that can significantly affect the convergence and effectiveness of neural networks. Therefore, we consider multiple-input and multiple-output (MIMO) AirComp FL systems with dynamic learning rate. First, we show the AirComp-Multicast duality between the AirComp problem in FL systems and the multicast problem in the downlink. We provide a low-complexity scheme with the subgradient approach after applying MM. Numerical results show that the aggregation error can vary dramatically in various fading channels, leading to large fluctuations in learning performance. Proposed algorithms are robust to varying channels and achieve prediction accuracy close to that of an ideal FL system without aggregation error.

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목차 (Table of Contents)

1 Introduction 1
1.1 Federated Learning 1
1.2 Over-the-Air Computation 8
1.3 Over-the-Air Federated Learning 15

1 Introduction 1
1.1 Federated Learning 1
1.2 Over-the-Air Computation 8
1.3 Over-the-Air Federated Learning 15
2 Device Selection for Over-the-Air Federated Learning 18
2.1 Over-the-Air FL System with Device Selection 19
2.1.1 System Model 19
2.1.2 Aggregation Noise in AirComp 22
2.1.3 Problem Formulation 25
2.2 Analysis of FL System with Device Selection 26
2.2.1 Device Selection with Random Beamforming 26
2.2.2 Convergence of FL with Device Selection 28
2.3 Sparse Optimization for Device Selection in FL 30
2.3.1 ℓ1-Norm Minimization Problem 30
2.3.2 KKT Conditions 33
2.4 Beamforming Vector Design 35
2.4.1 Convex Subproblems based on MM Approach 35
2.4.2 Low-Complexity Algorithm 37
2.4.3 Discussion of How Optimization Algorithm Works 40
2.5 Numerical Results 42
2.6 Summary 53
3 Device Selection in IRS-aided Over-the-Air FL 55
3.1 Over-the-Air FL System with IRS 56
3.1.1 System Model 56
3.2 Alternating Optimization of Beamforming Vector and Phase Shift 59
3.2.1 Optimizing Beamforming Vector 60
3.2.2 Optimizing Phase Shifts 61
3.3 Numerical Results 66
3.4 Summary 71
4 Joint Beamforming Vector Design and Learning Rate Optimization 72
4.1 Over-the-Air FL System with Dynamic Learning Rate 73
4.1.1 System Model 73
4.1.2 Problem Formulation 76
4.2 Effect of Multiple Antennas on Aggregation 78
4.3 Joint Design of Beamforming Vector and Dynamic Learning Rate 82
4.3.1 Convex Subproblems based on MM Approach 82
4.3.2 Low-Complexity Algorithm 83
4.4 Numerical Results 86
4.5 Summary 91
5 Conclusions 92
Appendix 94
Bibliography 103

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