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

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 artificial intelligence (AI)-driven physical systems, can fundamentally undermine their efficiency guarantees and lead to dangerous underestimation without being 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.

Funding: This work was supported by the National Science Foundation Division of Civil, Mechanical and Manufacturing Innovation [Grant CMMI-1834710], Division of Information and Intelligent Systems [Grants IIS-1849280 and IIS-1849304], Division of Computer and Network Systems [Grant CNS-2047454], and the Columbia Innovation Hub Award.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2021.0699.