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We consider the large sum of DC (Difference of Convex) functions minimizationproblem which appear in several different areas, especially in stochasticoptimization and machine learning. Two DCA (DC Algorithm) based algorithms areproposed: stochastic DCA and inexact stochastic DCA. We prove that theconvergence of both algorithms to a critical point is guaranteed withprobability one. Furthermore, we develop our stochastic DCA for solving animportant problem in multi-task learning, namely group variables selection inmulti class logistic regression. The corresponding stochastic DCA is veryinexpensive, all computations are explicit. Numerical experiments on severalbenchmark datasets and synthetic datasets illustrate the efficiency of ouralgorithms and their superiority over existing methods, with respect toclassification accuracy, sparsity of solution as well as running time.

Stochastic DCA for minimizing a large sum of DC functions with application to Multi-class Logistic Regression