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A recent article introduced thecontinuous stochastic gradient method (CSG)for the efficient solution of a class of stochastic optimization problems.While the applicability of known stochastic gradient type methods is typicallylimited to expected risk functions, no such limitation exists for CSG. Thisadvantage stems from the computation of design dependent integration weights,allowing for optimal usage of available information and therefore strongerconvergence properties. However, the nature of the formula used for theseintegration weights essentially limited the practical applicability of thismethod to problems in which stochasticity enters via a low-dimensional andsufficiently simple probability distribution. In this paper we significantlyextend the scope of the CSG method by presenting alternative ways to calculatethe integration weights. A full convergence analysis for this new variant ofthe CSG method is presented and its efficiency is demonstrated in comparison tomore classical stochastic gradient methods by means of a number of problemclasses relevant to stochastic optimization and machine learning.

CSG: A stochastic gradient method for a wide class of optimization problems appearing in a machine learning or data-driven context