Enhanced Importance Sampling through Latent Space Exploration in Normalizing Flows

TL;DR

This paper introduces a novel importance sampling method that updates the proposal distribution in the latent space of normalizing flows, improving rare event simulation efficiency in complex robotics scenarios.

Contribution

It proposes a new approach for importance sampling by leveraging latent space exploration in normalizing flows, enhancing sampling effectiveness for rare events.

Findings

Improved sampling efficiency in simulated robotics tasks.

Effective coverage of target distribution tails.

Enhanced estimation accuracy for rare events.

Abstract

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.