Sphere Packings, Lattices and Groups

The stringent requirements for low-latency and privacy of the emerging high-stake applications with intelligent devices such as drones and smart vehicles make the cloud computing inapplicable in these scenarios. Instead, edge machine learning becomes increasingly attractive for performing training and inference directly at network edges without sending data to a centralized data center. This stimulates a nascent field termed as federated learning for training a machine learning model on computation, storage, energy and bandwidth limited mobile devices in a distributed manner. To preserve data privacy and address the issues of unbalanced and non-IID data points across different devices, the federated averaging algorithm has been proposed for global model aggregation by computing the weighted average of locally updated model at each selected device. However, the limited communication bandwidth becomes the main bottleneck for aggregating the locally computed updates. We thus propose a novel over-the-air computation based approach for fast global model aggregation via exploring the superposition property of a wireless multiple-access channel. This is achieved by joint device selection and beamforming design, which is modeled as a sparse and low-rank optimization problem to support efficient algorithms design. To achieve this goal, we provide a difference-of-convex-functions (DC) representation for the sparse and low-rank function to enhance sparsity and accurately detect the fixed-rank constraint in the procedure of device selection. A DC algorithm is further developed to solve the resulting DC program with global convergence guarantees. The algorithmic advantages and admirable performance of the proposed methodologies are demonstrated through extensive numerical results.

Federated Learning via Over-the-Air Computation

The recent revival of AI is revolutionizing almost every branch of science and technology. Given the ubiquitous smart mobile gadgets and IoT devices, it is expected that a majority of intelligent applications will be deployed at the edge of wireless networks. This trend has generated strong interest in realizing an "intelligent edge" to support AI-enabled applications at various edge devices. Accordingly, a new research area, called edge learning, has emerged, which crosses and revolutionizes two disciplines: wireless communication and machine learning. A major theme in edge learning is to overcome the limited computing power, as well as limited data, at each edge device. This is accomplished by leveraging the mobile edge computing platform and exploiting the massive data distributed over a large number of edge devices. In such systems, learning from distributed data and communicating between the edge server and devices are two critical and coupled aspects, and their fusion poses many new research challenges. This article advocates a new set of design guidelines for wireless communication in edge learning, collectively called learning- driven communication. Illustrative examples are provided to demonstrate the effectiveness of these design guidelines. Unique research opportunities are identified.

Toward an Intelligent Edge: Wireless Communication Meets Machine Learning

Motivated by the increasing computational capacity of wireless user equipments (UEs), e.g., smart phones, tablets, or vehicles, as well as the increasing concerns about sharing private data, a new machine learning model has emerged, namely federated learning (FL), that allows a decoupling of data acquisition and computation at the central unit. Unlike centralized learning taking place in a data center, FL usually operates in a wireless edge network where the communication medium is resource-constrained and unreliable. Due to limited bandwidth, only a portion of UEs can be scheduled for updates at each iteration. Due to the shared nature of the wireless medium, transmissions are subjected to interference and are not guaranteed. The performance of FL system in such a setting is not well understood. In this paper, an analytical model is developed to characterize the performance of FL in wireless networks. Particularly, tractable expressions are derived for the convergence rate of FL in a wireless setting, accounting for effects from both scheduling schemes and inter-cell interference. Using the developed analysis, the effectiveness of three different scheduling policies, i.e., random scheduling (RS), round robin (RR), and proportional fair (PF), are compared in terms of FL convergence rate. It is shown that running FL with PF outperforms RS and RR if the network is operating under a high signal-to-interference-plus-noise ratio (SINR) threshold, while RR is more preferable when the SINR threshold is low. Moreover, the FL convergence rate decreases rapidly as the SINR threshold increases, thus confirming the importance of compression and quantization of the update parameters. The analysis also reveals a trade-off between the number of scheduled UEs and subchannel bandwidth under a fixed amount of available spectrum.

Scheduling Policies for Federated Learning in Wireless Networks

In this paper, the problem of energy efficient transmission and computation resource allocation for federated learning (FL) over wireless communication networks is investigated. In the considered model, each user exploits limited local computational resources to train a local FL model with its collected data and, then, sends the trained FL model to a base station (BS) which aggregates the local FL model and broadcasts it back to all of the users. Since FL involves an exchange of a learning model between users and the BS, both computation and communication latencies are determined by the learning accuracy level. Meanwhile, due to the limited energy budget of the wireless users, both local computation energy and transmission energy must be considered during the FL process. This joint learning and communication problem is formulated as an optimization problem whose goal is to minimize the total energy consumption of the system under a latency constraint. To solve this problem, an iterative algorithm is proposed where, at every step, closed-form solutions for time allocation, bandwidth allocation, power control, computation frequency, and learning accuracy are derived. Since the iterative algorithm requires an initial feasible solution, we construct the completion time minimization problem and a bisection-based algorithm is proposed to obtain the optimal solution, which is a feasible solution to the original energy minimization problem. Numerical results show that the proposed algorithms can reduce up to 59.5% energy consumption compared to the conventional FL method.

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Energy Efficient Federated Learning Over Wireless Communication Networks

Federated edge learning (FEEL) is a popular framework for model training at an edge server using data distributed at edge devices (e.g., smart-phones and sensors) without compromising their privacy. In the FEEL framework, edge devices periodically transmit high-dimensional stochastic gradients to the edge server, where these gradients are aggregated and used to update a global model. When the edge devices share the same communication medium, the multiple access channel (MAC) from the devices to the edge server induces a communication bottleneck. To overcome this bottleneck, an efficient broadband analog transmission scheme has been recently proposed, featuring the aggregation of analog modulated gradients (or local models) via the waveform-superposition property of the wireless medium. However, the assumed linear analog modulation makes it difficult to deploy this technique in modern wireless systems that exclusively use digital modulation. To address this issue, we propose in this work a novel digital version of broadband over-the-air aggregation, called one-bit broadband digital aggregation (OBDA). The new scheme features one-bit gradient quantization followed by digital quadrature amplitude modulation (QAM) at edge devices and over-the-air majority-voting based decoding at edge server. We provide a comprehensive analysis of the effects of wireless channel hostilities (channel noise, fading, and channel estimation errors) on the convergence rate of the proposed FEEL scheme. The analysis shows that the hostilities slow down the convergence of the learning process by introducing a scaling factor and a bias term into the gradient norm. However, we show that all the negative effects vanish as the number of participating devices grows, but at a different rate for each type of channel hostility.

One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis

Edge machine learning involves the deployment of learning algorithms at the network edge to leverage massive distributed data and computation resources to train artificial intelligence (AI) models. Among others, the framework of federated edge learning (FEEL) is popular for its data-privacy preservation. FEEL coordinates global model training at an edge server and local model training at devices that are connected by wireless links. This work contributes to the energy-efficient implementation of FEEL in wireless networks by designing joint computation-and-communication resource management (C2RM). The design targets the state-of-the-art heterogeneous mobile architecture where parallel computing using both CPU and GPU, called heterogeneous computing, can significantly improve both the performance and energy efficiency. To minimize the sum energy consumption of devices, we propose a novel C2RM framework featuring multi-dimensional control including bandwidth allocation, CPU-GPU workload partitioning and speed scaling at each device, and C2 time division for each link. The key component of the framework is a set of equilibriums in energy rates with respect to different control variables that are proved to exist among devices or between processing units at each device. The results are applied to designing efficient algorithms for computing the optimal C2RM policies faster than the standard optimization tools. Based on the equilibriums, we further design energy-efficient schemes for device scheduling and greedy spectrum sharing that scavenges “spectrum holes" resulting from heterogeneous C2 time divisions among devices. Using a real dataset, experiments are conducted to demonstrate the effectiveness of C2RM on improving the energy efficiency of a FEEL system.

Energy-Efficient Resource Management for Federated Edge Learning with CPU-GPU Heterogeneous Computing

Edge machine learning involves the deployment of learning algorithms at the wireless network edge so as to leverage massive mobile data for enabling intelligent applications. The mainstream edge learning approach, federated learning, has been developed based on distributed gradient descent. Based on the approach, stochastic gradients are computed at edge devices and then transmitted to an edge server for updating a global AI model. Since each stochastic gradient is typically high-dimensional, communication overhead becomes a bottleneck for edge learning. To address this issue, we propose a novel framework of hierarchical gradient quantization and study its effect on the learning performance. First, the framework features a practical hierarchical architecture for decomposing the stochastic gradient into its norm and normalized block gradients, and efficiently quantizes them using a uniform quantizer and a low-dimensional Grassmannian codebook, respectively. Subsequently, the quantized normalized block gradients are scaled and cascaded to yield the quantized normalized stochastic gradient using a socalled hinge vector, which is compressed using another low-dimensional Grassmannian quantizer designed under the criterion of minimum distortion. The other feature of the framework is a bit-allocation scheme for reducing the distortion, which divides the total quantization bits to determine the resolutions of low-dimensional quantizers. The framework is proved to guarantee model convergency by analyzing the convergence rate as a function of quantization bits. Furthermore, by simulation, our design is shown to substantially reduce the communication overhead compared with the state-of-the-art signSGD scheme, while achieving similar learning accuracies.

High-Dimensional Stochastic Gradient Quantization for Communication-Efficient Edge Learning

Edge machine learning involves the deployment of machine learning algorithms at the network edge so as to leverage massive mobile data and distributed computation resources. Many edge learning frameworks (e.g., federated learning) have been developed based on distributed gradient descent. Based on the approach, stochastic gradients are computed at edge devices and then transmitted to an edge server for aggregation for updating a global AI model. Since each gradient is typically high-dimensional (with millions to billions of coefficients), communication overhead may become a bottleneck for edge learning. In this work, we propose a novel gradient compression scheme to reduce the aforementioned overhead. Specifically, in the proposed scheme, the norm of the stochastic gradient is quantized using a uniform quantizer while the normalized stochastic gradient is decomposed into block gradients. A Grassmannian codebook is applied to quantizing each normalized block gradients. Their quantized versions are assembled using a so-called hinge vector, which is quantized using another Grassmannian codebook. Furthermore, a practical bit-allocation strategy is developed. By simulations, we show that similar learning performance can be achieved with substantially lower communication overhead as compared to the one-bit scalar quantization schemes used in the state-of-the-art design, namely signed SGD.

Yuqing Du

Papers

Toward an Intelligent Edge: Wireless Communication Meets Machine Learning

One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis

Energy-Efficient Resource Management for Federated Edge Learning with CPU-GPU Heterogeneous Computing

High-Dimensional Stochastic Gradient Quantization for Communication-Efficient Edge Learning

High-Dimensional Stochastic Gradient Quantization for Communication-Efficient Edge Learning