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We study unconstrained optimization problems with nonsmooth and convexobjective function in the form of a mathematical expectation. The proposedmethod approximates the expected objective function with a sample averagefunction using Inexact Restoration-based adapted sample sizes. The sample sizeis chosen in an adaptive manner based on Inexact Restoration. The algorithmuses line search and assumes descent directions with respect to the currentapproximate function. We prove the a.s. convergence under standard assumptions.Numerical results for two types of problems, machine learning loss function fortraining classifiers and stochastic linear complementarity problems, prove theefficiency of the proposed scheme.

An inexact restoration-nonsmooth algorithm with variable accuracy for  stochastic nonsmooth convex optimization problems in machine learning and  stochastic linear complementarity problems