Solving decision problems in complex, stochastic environments is often achieved by estimating the expected outcome of decisions via Monte Carlo sampling. However, sampling may overlook rare, but important events, which can severely impact the decision making process. We present a method in which a Normalizing Flow generative model is trained to simulate samples directly from a conditional distribution given that a rare event occurs. By utilizing Coupling Flows, our model can, in principle, approximate any sampling distribution arbitrarily well. By combining the approximation method with Importance Sampling, highly accurate estimates of complicated integrals and expectations can be obtained. We include several examples to demonstrate how the method can be used for efficient sampling and estimation, even in high-dimensional and rare-event settings. We illustrate that by simulating directly from a rare-event distribution significant insight can be gained into the way rare events happen.

翻译：解决复杂随机环境中的决策问题，通常通过蒙特卡洛采样估计决策的预期结果来实现。然而，采样可能会忽略稀有但重要的事件，从而严重影响决策过程。我们提出了一种方法，其中训练一个归一化流生成模型，在给定稀有事件发生的条件下直接从条件分布中模拟样本。通过利用耦合流，我们的模型原则上可以任意近似任何采样分布。将该近似方法与重要性采样相结合，可以获得复杂积分和期望的高精度估计。我们通过多个示例展示了该方法如何用于高效采样和估计，即使在高维和稀有事件场景中也是如此。我们表明，通过直接从稀有事件分布进行模拟，可以深入了解稀有事件发生的方式。