  In this paper, for solving a broad class of large-scale nonconvex and
nonsmooth optimization problems, we propose a stochastic two step inertial
Bregman proximal alternating linearized minimization (STiBPALM) algorithm with
variance-reduced stochastic gradient estimators. And we show that SAGA and
SARAH are variance-reduced gradient estimators. Under expectation conditions
with the Kurdyka-Lojasiewicz property and some suitable conditions on the
parameters, we obtain that the sequence generated by the proposed algorithm
converges to a critical point. And the general convergence rate is also
provided. Numerical experiments on sparse nonnegative matrix factorization and
blind image-deblurring are presented to demonstrate the performance of the
proposed algorithm.
