This paper provides an introductory overview of how one may employ importance sampling effectively as a tool for solving stochastic optimization formulations incorporating tail risk measures such as Conditional Value-at-Risk. Approximating the tail risk measure by its sample average approximation, while appealing due to its simplicity and universality in use, requires a large number of samples to be able to arrive at risk-minimizing decisions with high confidence. This is primarily due to the rarity with which the relevant tail events get observed in the samples. In simulation, Importance Sampling is among the most prominent methods for substantially reducing the sample requirement while estimating probabilities of rare events. Can importance sampling be used for optimization as well? If so, what are the ingredients required for making importance sampling an effective tool for optimization formulations involving rare events? This tutorial aims to provide an introductory overview of the two key ingredients in this regard, namely, (i) how one may arrive at an importance sampling change of measure prescription at every decision, and (ii) the prominent techniques available for integrating such a prescription within a solution paradigm for stochastic optimization formulations.

翻译：本文旨在初步介绍如何有效利用重要性采样作为工具，解决涉及尾部风险度量（如条件风险价值）的随机优化问题。虽然通过样本均值近似来逼近尾部风险度量因其简单性和通用性而具有吸引力，但为了以高置信度获得风险最小化决策，需要大量样本。这主要是由于相关尾部事件在样本中观测到的稀有性。在仿真中，重要性采样是显著降低稀有事件概率估计所需样本量的最突出方法之一。重要性采样能否也用于优化？如果可以，使重要性采样成为涉及稀有事件的优化问题的有效工具需要哪些要素？本教程旨在初步介绍与此相关的两个关键要素，即：(i) 如何在每个决策点得出重要性采样的测度变换方案，以及(ii) 将该方案整合到随机优化问题求解框架中的突出技术。