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

Abstract

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.

A Survey on Safety-Critical Driving Scenario Generation -- A Methodological Perspective

“…[122] uses GMM for IS distribution and further analyzes the efficiency of GMM based IS distribution for random forest and neural network classifiers [123]. ReLUactivated deep neural network is considered in [124] to estimate the dangerous set and compute an IS estimator for a risk upper bound for Gaussian case, with a more general case presented in [54]. The Adaptive IS approach is used to construct adversarial environments to accelerate policy evaluation [125].…”

Test Against High-Dimensional Uncertainties: Accelerated Evaluation of Autonomous Vehicles with Deep Importance Sampling

“…The relaxation is proposed using a simple parametric class to include piecewise models in [36], [37] and Gaussian Mixture Models in [26] with theoretical guarantees provided in [38] adopting the dominating point idea along with iterative cutting plane methods. [27] applies the method for black-box systems, computing an upperbound for the failure probability of the system with an efficiency guarantee. The limitation of existing studies is that they all focus on developing methods for relatively low-dimensional decision-making algorithms usually based on control theories and decision trees which have been lagged behind by the increasingly complex AI algorithms, e.g.…”

“…as objective. More general formulation is available in the literature, for instance formulation in [27]. Solve the optimization problem…”

“…The main limitation of these methods is that they can only handle a low-dimensional problem and requires some level of information of the underlying systems. An extension that could be used for complex or black-box systems is proposed in [27], but can only be used to estimate an upper-bound for the target risk metric.…”

“…In this work, we adopt the risk upper-bound estimator from [27] to compute a less biased estimator to solve the evaluation task. This is particularly important for evaluating and comparing the safety of AV prototypes whose performances are often really close to one another.…”