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Evaluating the reliability of intelligent physical systems against raresafety-critical events poses a huge testing burden for real-world applications.Simulation provides a useful platform to evaluate the extremal risks of thesesystems before their deployments. Importance Sampling (IS), while proven to bepowerful for rare-event simulation, faces challenges in handling theselearning-based systems due to their black-box nature that fundamentallyundermines its efficiency guarantee, which can lead to under-estimation withoutdiagnostically detected. We propose a framework called Deep ProbabilisticAccelerated Evaluation (Deep-PrAE) to design statistically guaranteed IS, byconverting black-box samplers that are versatile but could lack guarantees,into one with what we call a relaxed efficiency certificate that allowsaccurate estimation of bounds on the safety-critical 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 of anintelligent driving algorithm.

Deep Probabilistic Accelerated Evaluation: A Robust Certifiable Rare-Event Simulation Methodology for Black-Box Safety-Critical Systems