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Evaluating the reliability of intelligent physical systems against rare safety-critical events poses a huge testing burden for real-world applications. Simulation provides a useful platform to evaluate the extremal risks of these systems before their deployments. Importance Sampling (IS), while proven to be powerful for rare-event simulation, faces challenges in handling these learning-based systems due to their black-box nature that fundamentally undermines its efficiency guarantee, which can lead to 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 safety-critical 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 an intelligent driving algorithm.
Increasingly sophisticated mathematical modelling processes from Machine Learning are being used to analyse complex data. However, the performance and explainability of these models within practical critical systems requires a rigorous and continuous
We consider the problem of controlling an unknown linear time-invariant dynamical system from a single chain of black-box interactions, with no access to resets or offline simulation. Under the assumption that the system is controllable, we give the
We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, $T subseteq mathbb{R}^m$, we study the probability w.r.t. the BNN posterior that all the points in $T$ are m
Autonomous and semi-autonomous systems for safety-critical applications require rigorous testing before deployment. Due to the complexity of these systems, formal verification may be impossible and real-world testing may be dangerous during developme
Most existing black-box optimization methods assume that all variables in the system being optimized have equal cost and can change freely at each iteration. However, in many real world systems, inputs are passed through a sequence of different opera