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This paper considers optimization problems where the objective is the sum ofa function given by an expectation and a closed convex composite function, andproposes stochastic composite proximal bundle (SCPB) methods for solving it.Complexity guarantees are established for them without requiring knowledge ofparameters associated with the problem instance. Moreover, it is shown thatthey have optimal complexity when these problem parameters are known. To thebest of our knowledge, this is the first proximal bundle method for stochasticprogramming able to deal with continuous distributions. Finally, we presentcomputational results showing that SCPB substantially outperforms the robuststochastic approximation (RSA) method in all instances considered.

A single cut proximal bundle method for stochastic convex composite optimization