Overconservativeness of Variance-Based Efficiency Criteria and Probabilistic Efficiency in Rare-Event Simulation

Yuanlu Bai (), Zhiyuan Huang (), Henry Lam () and Ding Zhao ()
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Yuanlu Bai: Columbia University, New York, New York 10027
Zhiyuan Huang: Tongji University, Shanghai 200092, China
Henry Lam: Columbia University, New York, New York 10027
Ding Zhao: Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

Management Science, 2024, vol. 70, issue 10, 6852-6873

Abstract: 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, the 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.

Keywords: rare-event simulation; importance sampling; relative error; large deviations; dominating points (search for similar items in EconPapers)
Date: 2024
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