  In this paper, we propose a bootstrap method applied to massive data
processed distributedly in a large number of machines. This new method is
computationally efficient in that we bootstrap on the master machine without
over-resampling, typically required by existing methods
\cite{kleiner2014scalable,sengupta2016subsampled}, while provably achieving
optimal statistical efficiency with minimal communication. Our method does not
require repeatedly re-fitting the model but only applies multiplier bootstrap
in the master machine on the gradients received from the worker machines.
Simulations validate our theory.
