A single cut proximal bundle method for stochastic convex composite optimization

In this paper, we consider optimization problems where the objective is the sum of a function given by an expectation and a closed convex composite function. For such problems, we propose a stochastic composite proximal bundle (SCPB) method with optimal complexity. The method does not require estimation of parameters involved in the assumptions on the objective functions. Moreover, to the best of our knowledge, this is the first proximal bundle method for stochastic programming able to deal with continuous distributions. Finally, we present computational results showing that SCPB substantially outperforms the robust stochastic approximation method on all instances considered.