  We propose and study a novel stochastic inertial primal-dual approach to
solve composite optimization problems. These latter problems arise naturally
when learning with penalized regularization schemes. Our analysis provide
convergence results in a general setting, that allows to analyze in a unified
framework a variety of special cases of interest. Key in our analysis is
considering the framework of splitting algorithm for solving a monotone
inclusions in suitable product spaces and for a specific choice of
preconditioning operators.
