  In this note we propose a new variant of the hybrid variance-reduced proximal
gradient method in [7] to solve a common stochastic composite nonconvex
optimization problem under standard assumptions. We simply replace the
independent unbiased estimator in our hybrid- SARAH estimator introduced in [7]
by the stochastic gradient evaluated at the same sample, leading to the
identical momentum-SARAH estimator introduced in [2]. This allows us to save
one stochastic gradient per iteration compared to [7], and only requires two
samples per iteration. Our algorithm is very simple and achieves optimal
stochastic oracle complexity bound in terms of stochastic gradient evaluations
(up to a constant factor). Our analysis is essentially inspired by [7], but we
do not use two different step-sizes.
