  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.
