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arXiv · 2012.03844

Adaptive sampling strategies for risk-averse stochastic optimization with constraints

Florian Beiser·Brendan Keith·Simon Urbainczyk·Barbara Wohlmuth
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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.

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Florian Beiser, Brendan Keith, Simon Urbainczyk, Barbara Wohlmuth. 2020-12-07. Adaptive sampling strategies for risk-averse stochastic optimization with constraints. https://doi.org/10.1093/imanum%2Fdrac083

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