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Rare-event simulation techniques, such as importance sampling (IS),constitute powerful tools to speed up challenging estimation of rarecatastrophic events. These techniques often leverage the knowledge and analysison underlying system structures to endow desirable efficiency guarantees.However, black-box problems, especially those arising from recentsafety-critical applications of AI-driven physical systems, can fundamentallyundermine their efficiency guarantees and lead to dangerous under-estimationwithout diagnostically detected. We propose a framework called DeepProbabilistic Accelerated Evaluation (Deep-PrAE) to design statisticallyguaranteed IS, by converting black-box samplers that are versatile but couldlack guarantees, into one with what we call a relaxed efficiency certificatethat allows accurate estimation of bounds on the rare-event probability. Wepresent the theory of Deep-PrAE that combines the dominating point concept withrare-event set learning via deep neural network classifiers, and demonstrateits effectiveness in numerical examples including the safety-testing ofintelligent driving algorithms.

Certifiable Deep Importance Sampling for Rare-Event Simulation of Black-Box Systems