A single cut proximal bundle method for stochastic convex composite optimization

TL;DR

This paper introduces a novel stochastic composite proximal bundle method capable of handling continuous distributions in stochastic convex optimization, providing optimal complexity guarantees and outperforming existing methods in computational tests.

Contribution

It presents the first proximal bundle method for stochastic programming with continuous distributions, offering complexity guarantees without prior parameter knowledge.

Findings

SCPB outperforms RSA in computational experiments

Provides optimal complexity when problem parameters are known

First method to handle continuous distributions in this context

Abstract

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.