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 (with millions to billions of
coefficients), communication overhead becomes a bottleneck for edge learning.
To address this issue, we propose in this work a novel framework of
hierarchical stochastic 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 codebook on a Grassmann manifold, respectively.
Subsequently, the quantized normalized block gradients are scaled and cascaded
to yield the quantized normalized stochastic gradient using a so-called hinge
vector designed under the criterion of minimum distortion. The hinge vector is
also efficiently compressed using another low-dimensional Grassmannian
quantizer. The other feature of the framework is a bit-allocation scheme for
reducing the quantization error. The scheme determines the resolutions of the
low-dimensional quantizers in the proposed framework. The framework is proved
to guarantee model convergency by analyzing the convergence rate as a function
of the 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 both achieve similar learning
accuracies.

本文提出了一种基于分层随机梯度量化的边缘机器学习框架，并研究了其对学习性能的影响，包括量化误差和通信开销的降低。该方案采用了分层结构和基于矢量的量化，同时引入了一个位分配方式来保证量化精度，该方案能够在保证学习准确性的前提下显著减少通信开销。