arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2202.02812cs.LGcs.ITmath.IT
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有损梯度压缩:一个比特可以买到多少精度?

Lossy Gradient Compression: How Much Accuracy Can One Bit Buy?

McMaster University(麦克马斯特大学);National Yang-Ming Chiao-Tung University(阳明交通大学)

Sadaf Salehkalaibar, Stefano Rini

摘要:

在联邦学习(FL)中,通过聚合从多个远程学习者获得的模型更新来在参数服务器(PS)处训练全局模型。通常,远程用户和PS之间的通信是速率受限的,而从PS到远程用户的传输是不受约束的。FL设置引起分布式学习场景,其中来自远程学习者的更新必须被压缩,以便满足朝向PS的上行链路传输中的通信速率约束。对于这个问题,人们希望压缩模型更新,以便最小化由压缩误差导致的准确性损失。在本文中,我们采用率失真方法来解决深度神经网络(DNN)分布式训练的压缩器设计问题。特别是,我们定义了一个衡量的压缩性能下的通信速率约束-的\emph{per-bit accuracy} -这解决了最终的精度提高,一个位的通信带来的集中式模型。为了最大化每比特的准确性,我们考虑将远程学习者的DNN梯度更新建模为广义正态分布。在DNN梯度分布的假设下,我们提出了一类失真度量,以帮助设计用于压缩模型更新的量化器。我们认为,这个家庭的失真措施,我们称为“$M$ -幅度加权$L_2$“规范,抓住了从业者的直觉在梯度压缩机的选择。数值模拟提供CIFAR-10数据集验证所提出的方法。

英文摘要:

In federated learning (FL), a global model is trained at a Parameter Server (PS) by aggregating model updates obtained from multiple remote learners. Generally, the communication between the remote users and the PS is rate-limited, while the transmission from the PS to the remote users are unconstrained. The FL setting gives rise to the distributed learning scenario in which the updates from the remote learners have to be compressed so as to meet communication rate constraints in the uplink transmission toward the PS. For this problem, one wishes to compress the model updates so as to minimize the loss in accuracy resulting from the compression error. In this paper, we take a rate-distortion approach to address the compressor design problem for the distributed training of deep neural networks (DNNs). In particular, we define a measure of the compression performance under communication-rate constraints -- the \emph{per-bit accuracy} -- which addresses the ultimate improvement of accuracy that a bit of communication brings to the centralized model. In order to maximize the per-bit accuracy, we consider modeling the DNN gradient updates at remote learners as a generalized normal distribution. Under this assumption on the DNN gradient distribution, we propose a class of distortion measures to aid the design of quantizers for the compression of the model updates. We argue that this family of distortion measures, which we refer to as "$M$-magnitude weighted $L_2$" norm, captures the practitioner's intuition in the choice of gradient compressor. Numerical simulations are provided to validate the proposed approach for the CIFAR-10 dataset.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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