  In this paper, we propose a stochastic method for solving equality
constrained optimization problems that utilizes predictive variance reduction.
Specifically, we develop a method based on the sequential quadratic programming
paradigm that employs variance reduction in the gradient approximations. Under
reasonable assumptions, we prove that a measure of first-order stationarity
evaluated at the iterates generated by our proposed algorithm converges to zero
in expectation from arbitrary starting points, for both constant and adaptive
step size strategies. Finally, we demonstrate the practical performance of our
proposed algorithm on constrained binary classification problems that arise in
machine learning.
