  This paper considers optimization problems where the objective is the sum of
a function given by an expectation and a closed convex composite function, and
proposes stochastic composite proximal bundle (SCPB) methods for solving it.
Complexity guarantees are established for them without requiring knowledge of
parameters associated with the problem instance. Moreover, it is shown that
they have optimal complexity when these problem parameters are known. 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 (RSA) method in all instances considered.

Optimization and Control