We consider the problem where $n$ clients transmit $d$-dimensional real-valued vectors using only $d(1+o(1))$ bits each, in a manner that allows a receiver to approximately reconstruct their mean. Such compression problems arise in federated and distributed learning, as well as in other domains. We provide novel mathematical results and derive corresponding new algorithms that outperform previous compression algorithms in accuracy and computational efficiency. We evaluate our methods on a collection of distributed and federated learning tasks, using a variety of datasets, and show a consistent improvement over the state of the art.

翻译：我们考虑了这样的问题:一美元客户只用每张(1+o(1))美元来传输以美元计算的维维值实际值矢量,使接收者能够大致重建其平均值。这种压缩问题出现在联盟和分布式学习以及其他领域。我们提供了新的数学结果,并得出了在准确性和计算效率方面比以往压缩算法更好的相应的新算法。我们利用各种数据集,评估了我们收集分布式和联合学习任务的方法,并展示了与最新技术相比的不断进步。