  Rare-event simulation techniques, such as importance sampling (IS),
constitute powerful tools to speed up challenging estimation of rare
catastrophic events. These techniques often leverage the knowledge and analysis
on underlying system structures to endow desirable efficiency guarantees.
However, black-box problems, especially those arising from recent
safety-critical applications of AI-driven physical systems, can fundamentally
undermine their efficiency guarantees and lead to dangerous under-estimation
without diagnostically detected. We propose a framework called Deep
Probabilistic Accelerated Evaluation (Deep-PrAE) to design statistically
guaranteed IS, by converting black-box samplers that are versatile but could
lack guarantees, into one with what we call a relaxed efficiency certificate
that allows accurate estimation of bounds on the rare-event probability. We
present the theory of Deep-PrAE that combines the dominating point concept with
rare-event set learning via deep neural network classifiers, and demonstrate
its effectiveness in numerical examples including the safety-testing of
intelligent driving algorithms.
