论文标题
Wasserstein分布在强大的优化问题上的敏感性分析
Sensitivity analysis of Wasserstein distributionally robust optimization problems
论文作者
论文摘要
我们考虑对通用随机优化问题的敏感性来建模不确定性。我们采用一种非参数方法，并使用假定模型周围的Wasserstein Ball捕获模型的不确定性。我们为对值函数和优化器的一阶校正提供明确的公式，并将结果进一步扩展到线性约束下的优化。我们向统计，机器学习，数学金融和不确定性量化提供了应用。特别是，与普通的最小二乘回归相比，我们为方形拉索回归系数和推断系数收缩提供了明确的一阶近似。我们考虑呼叫选项定价的稳健性，并推断出新的黑色chcholes敏感性，这是所谓的Vega的非参数版本。我们还计算了财务中优化确定性等效物的敏感性，并提出了量化神经网络对对抗性例子的鲁棒性的措施。
We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for the first order correction to both the value function and the optimizer and further extend our results to optimization under linear constraints. We present applications to statistics, machine learning, mathematical finance and uncertainty quantification. In particular, we provide explicit first-order approximation for square-root LASSO regression coefficients and deduce coefficient shrinkage compared to the ordinary least squares regression. We consider robustness of call option pricing and deduce a new Black-Scholes sensitivity, a non-parametric version of the so-called Vega. We also compute sensitivities of optimized certainty equivalents in finance and propose measures to quantify robustness of neural networks to adversarial examples.
