论文标题
最大平均差异分布在有限样本保证的情况下可稳健的非线性偶然性约束优化
Maximum Mean Discrepancy Distributionally Robust Nonlinear Chance-Constrained Optimization with Finite-Sample Guarantee
论文作者
论文摘要
本文是通过使用受欢迎的Wasserstein歧义集在分配强大的机会约束程序（DRCCP）中解决的开放问题来激发的。具体而言，这些程序的计算技术通常使用昂贵的交叉验证（CV）程序或保守的度量浓度界限来设置限制性的限制性假设和Wasserstein歧义集的大小。相比之下，我们提出了一种使用内核最大平均差异（MMD）歧义集的实用DRCCP算法，我们将其称为MMD-DRCCP，以治疗一般的非线性约束，而无需使用临时重新印度。 MMD-DRCCP可以通过可靠的有限样本约束满意度来处理一般的非线性和非凸约限制，可保证尺寸独立于$ \ MATHCAL {O}（\ frac {1} {\ sqrt {n}}}} {\ sqrt {n}}）$ rate，可通过实用的Algorith Mathive。我们进一步提出了一种有效的自举计划，用于在实践中构建尖锐的MMD歧义集，而无需诉诸CV。我们的算法在投资组合优化问题上进行了数值验证，并具有基于非convex约束的基于管子的分布稳健模型预测性控制问题。
This paper is motivated by addressing open questions in distributionally robust chance-constrained programs (DRCCP) using the popular Wasserstein ambiguity sets. Specifically, the computational techniques for those programs typically place restrictive assumptions on the constraint functions and the size of the Wasserstein ambiguity sets is often set using costly cross-validation (CV) procedures or conservative measure concentration bounds. In contrast, we propose a practical DRCCP algorithm using kernel maximum mean discrepancy (MMD) ambiguity sets, which we term MMD-DRCCP, to treat general nonlinear constraints without using ad-hoc reformulation techniques. MMD-DRCCP can handle general nonlinear and non-convex constraints with a proven finite-sample constraint satisfaction guarantee of a dimension-independent $\mathcal{O}(\frac{1}{\sqrt{N}})$ rate, achievable by a practical algorithm. We further propose an efficient bootstrap scheme for constructing sharp MMD ambiguity sets in practice without resorting to CV. Our algorithm is validated numerically on a portfolio optimization problem and a tube-based distributionally robust model predictive control problem with non-convex constraints.
