Importance sampling (IS) is a powerful tool for rare-event estimation. However, in many settings, we need to estimate not only the performance expectation but also its gradient. In this paper, we build a bridge from the IS for rare-event estimation to gradient estimation. We establish that, for a class of problems, an efficient IS sampler for estimating the probability of the underlying rare event is also efficient for estimating gradients of expectations over the same rare-event set. We show that both the infinitesimal perturbation analysis and the likelihood ratio estimators can be studied under the proposed framework. We use two numerical examples to validate our findings.
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Importance Sampling for Rare-Event Gradient Estimation
Semantic Scholar · Mathematics · 2022
Abstract
Importance sampling (IS) is a powerful tool for rare-event estimation. However, in many settings, we need to estimate not only the performance expectation but also its gradient. In this paper, we build a bridge from the IS for rare-event estimation to gradient estimation. We establish that, for a class of problems, an efficient IS sampler for estimating the probability of the underlying rare event is also efficient for estimating gradients of expectations over the same rare-event set. We show that both the infinitesimal perturbation analysis and the likelihood ratio estimators can be studied under the proposed framework. We use two numerical examples to validate our findings.