Perturbed Iterate SGD for Lipschitz Continuous Loss Functions

This paper presents an extension of stochastic gradient descent for the minimization Lipschitz continuous loss functions. Our motivation is use in non-smooth non-convex optimization problems, which are frequently encountered applications such as machine learning. Using Clarke $$\epsilon $$ -subdifferential, we prove non-asymptotic convergence to approximate stationary point expectation proposed method. From this result, a method with high probability, well asymptotic almost surely developed. results hold under assumption that function Carathéodory everywhere decision variables. To best our knowledge, first analysis these minimal assumptions.