  We consider the minimization of a sum of a smooth function with a nonsmooth
composite function, where the composition is applied on a random linear
mapping. This random composite model encompasses many problems, and can
especially capture realistic scenarios in which the data is sampled during the
optimization process. We propose and analyze a method that combines the
classical Augmented Lagrangian framework with a sampling mechanism and adaptive
update of the penalty parameter. We show that every accumulation point of the
sequence produced by our algorithm is almost surely a critical point.
