# Over-Conservativeness of Variance-Based Efficiency Criteria and Probabilistic Efficiency in Rare-Event Simulation

arXiv: https://arxiv.org/abs/2110.12573 · HTML: https://mlsanity.com/paper/2110.12573/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2021.

## Built on by (most cited first, 1 of 1)

- [Test Against High-Dimensional Uncertainties: Accelerated Evaluation of Autonomous Vehicles with Deep Importance Sampling](https://mlsanity.com/paper/2204.02351/) (2022)

## Abstract (arXiv)

In rare-event simulation, an importance sampling (IS) estimator is regarded as efficient if its relative error, namely the ratio between its standard deviation and mean, is sufficiently controlled. It is widely known that when a rare-event set contains multiple "important regions" encoded by the so-called dominating points, IS needs to account for all of them via mixing to achieve efficiency. We argue that in typical experiments, missing less significant dominating points may not necessarily cause inefficiency, and the traditional analysis recipe could suffer from intrinsic looseness by using relative error, or in turn estimation variance, as an efficiency criterion. We propose a new efficiency notion, which we call probabilistic efficiency, to tighten this gap. In particular, we show that under the standard Gartner-Ellis large deviations regime, an IS that uses only the most significant dominating points is sufficient to attain this efficiency notion. Our finding is especially relevant in high-dimensional settings where the computational effort to locate all dominating points is enormous.