To main content

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.
Read the publication

Category

Academic article

Language

English

Author(s)

  • Florian Beiser
  • Brendan Keith
  • Simon Urbainczyk
  • Barbara Wohlmuth

Affiliation

  • SINTEF Digital / Mathematics and Cybernetics
  • Heriot-Watt University
  • Technical University of Munich
  • Brown University

Year

2023

Published in

IMA Journal of Numerical Analysis

ISSN

0272-4979

Volume

43

Issue

6

Page(s)

3729 - 3765

View this publication at Norwegian Research Information Repository