论文标题
对规避风险随机优化的自适应抽样策略和约束
Adaptive sampling strategies for risk-averse stochastic optimization with constraints
论文作者
论文摘要
我们引入了具有确定性约束的随机程序的自适应抽样方法。首先，我们提出和分析了随机投影梯度方法的变体，其中用于近似于减少梯度的样本大小在正常情况下确定和自适应更新。该方法适用于广泛的基于期望的风险措施，并导致用于估计目标功能梯度的个体梯度评估大大降低。预期风险最小化和有条件的价值最小化的数值实验支持了这一结论，并证明了风险中性和规避风险的问题的实际绩效和功效。其次，我们基于类似的自适应采样原理提出了一种SQP型方法。在简化的工程设计应用程序中证明了该方法的好处，该应用具有避免风险的钢壳结构的优化，但具有不确定的加载条件和模型不确定性。
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.
