Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows for more efficient estimation of rare events or tails of distributions. However, importance sampling can fail when the proposal distribution does not effectively cover the target distribution. In this work, we propose a method for more efficient sampling by updating the proposal distribution in the latent space of a normalizing flow. Normalizing flows learn an invertible mapping from a target distribution to a simpler latent distribution. The latent space can be more easily explored during the search for a proposal distribution, and samples from the proposal distribution are recovered in the space of the target distribution via the invertible mapping. We empirically validate our methodology on simulated robotics applications such as autonomous racing and aircraft ground collision avoidance.

翻译：重要性采样是一种用于蒙特卡洛模拟的稀有事件仿真技术，其通过使采样分布偏向感兴趣的稀有事件来实现。通过对采样点分配适当的权重，重要性采样能够更高效地估计稀有事件或分布的尾部。然而，当提议分布未能有效覆盖目标分布时，重要性采样可能会失效。在本工作中，我们提出了一种通过在归一化流的潜在空间中更新提议分布来实现更高效采样的方法。归一化流学习从目标分布到更简单的潜在分布的可逆映射。在搜索提议分布的过程中，可以更容易地探索潜在空间，并且通过该可逆映射，提议分布的样本可以在目标分布的空间中被恢复。我们在模拟机器人学应用（如自主竞速和飞机地面防撞）上对我们的方法进行了实证验证。