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Distributional Robustness Analysis for Nonlinear Uncertainty Structures

机译：非线性不确定结构的分布鲁棒性分析

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摘要

One of the main objectives of this note is to address the question: what is the worst-case expected value of a continuous function (worst-case performance) over a class of admissible distributions? In this note, the class of symmetric and non-increasing distributions is considered and results are provided for the class of so-called semi-algebraic functions. The first part of the note shows that, for the class of distributions considered, it suffices to solve a convex optimization problem for which efficient linear matrix inequality (LMI) relaxations are available. Secondly, the proposed approach is applied to estimate hard bounds on the worst-case probability of a semi-algebraic function being negative. Several numerical examples are presented which illustrate the effectiveness of the approach presented.
机译：本说明的主要目的之一是解决以下问题：在一类可允许的分布范围内，连续函数（最坏情况的性能）的最坏情况预期值是多少？在本说明中，考虑了对称分布和非递增分布的类别，并为所谓的半代数函数提供了结果。注释的第一部分表明，对于所考虑的分布类别，足以解决凸优化问题，对于该凸优化问题，可以使用有效的线性矩阵不等式（LMI）松弛。其次，将所提出的方法用于估计半代数函数为负的最坏情况概率的硬边界。给出了几个数值示例，说明了所提出方法的有效性。

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