DRIVE: One-bit Distributed Mean Estimation

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.