Adaptive sampling strategies for risk-averse stochastic optimization with constraints

• Published in: IMA journal of numerical analysis Vol. 43; no. 6; pp. 3729 - 3765
• Main Authors: Beiser, Florian, Keith, Brendan, Urbainczyk, Simon, Wohlmuth, Barbara
• Format: Journal Article
• Language: English
• Published: Oxford University Press 04.11.2023
• Subjects: sample size selection; portfolio optimization; shape optimization; constrained optimization; stochastic optimization
• ISSN: 0272-4979; 1464-3642
• DOI: 10.1093/imanum/drac083

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.