  We propose a stochastic optimization method for the minimization of the sum
of three convex functions, one of which has Lipschitz continuous gradient as
well as restricted strong convexity. Our approach is most suitable in the
setting where it is computationally advantageous to process smooth term in the
decomposition with its stochastic gradient estimate and the other two functions
separately with their proximal operators, such as doubly regularized empirical
risk minimization problems. We prove the convergence characterization of the
proposed algorithm in expectation under the standard assumptions for the
stochastic gradient estimate of the smooth term. Our method operates in the
primal space and can be considered as a stochastic extension of the
three-operator splitting method. Numerical evidence supports the effectiveness
of our method in real-world problems.
