Adaptive sampling strategies for risk-averse stochastic optimization with constraints
Abstract
We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced gradient is determined on-the-fly and updated adaptively. This method is applicable to a broad class of expectation-based risk measures and leads to a significant reduction in the individual gradient evaluations used to estimate the objective function gradient. Numerical experiments with expected risk minimization and conditional value-at-risk minimization support this conclusion and demonstrate practical performance and efficacy for both risk-neutral and risk-averse problems. Second, we propose an SQP-type method based on similar adaptive sampling principles. The benefits of this method are demonstrated in a simplified engineering design application featuring risk-averse shape optimization of a steel shell structure subject to uncertain loading conditions and model uncertainty.
Cite
@article{arxiv.2012.03844,
title = {Adaptive sampling strategies for risk-averse stochastic optimization with constraints},
author = {Florian Beiser and Brendan Keith and Simon Urbainczyk and Barbara Wohlmuth},
journal= {arXiv preprint arXiv:2012.03844},
year = {2023}
}