  We consider the large sum of DC (Difference of Convex) functions minimization
problem which appear in several different areas, especially in stochastic
optimization and machine learning. Two DCA (DC Algorithm) based algorithms are
proposed: stochastic DCA and inexact stochastic DCA. We prove that the
convergence of both algorithms to a critical point is guaranteed with
probability one. Furthermore, we develop our stochastic DCA for solving an
important problem in multi-task learning, namely group variables selection in
multi class logistic regression. The corresponding stochastic DCA is very
inexpensive, all computations are explicit. Numerical experiments on several
benchmark datasets and synthetic datasets illustrate the efficiency of our
algorithms and their superiority over existing methods, with respect to
classification accuracy, sparsity of solution as well as running time.
