While recent developments in autonomous vehicle (AV) technology highlight substantial progress, we lack tools for rigorous and scalable testing. Real-world testing, the de facto evaluation environment, places the public in danger, and, due to the rare nature of accidents, will require billions of miles in order to statistically validate performance claims. We implement a simulation framework that can test an entire modern autonomous driving system, including, in particular, systems that employ deep-learning perception and control algorithms. Using adaptive sampling methods to accelerate rare-event probability evaluation, we estimate the probability of an accident under a base distribution governing standard traffic behavior. We demonstrate our framework on a highway scenario. Several fatal accidents involving autonomous vehicles (AVs) underscore the importance of testing whether AV perception and control pipelines-when considered as a whole systemcan safely interact with other human traffic participants. Unfortunately, testing AVs in real environments, the most straightforward validation framework for system-level inputoutput behavior, requires prohibitive amounts of time due to the rare nature of serious accidents BID22 . Concretely, a recent study BID8 argues that AVs need to drive "hundreds of millions of miles, and, under some scenarios, hundreds of billions of miles to create enough data to clearly demonstrate their safety." On the other hand, formally verifying an AV algorithm's "correctness" BID11 BID0 BID21 BID13 is inherently difficult because all driving policies are subject to crashes caused by other drivers BID22 . Ruling out scenarios where the AV should not be blamed for such accidents is a task subject to logical inconsistency and subjective assignment of fault.Motivated by the challenges underlying real-world testing and formal verification, we consider a probabilistic paradigmwhich we describe as a risk-based framework BID14 -where the goal is to evaluate the probability of an accident under a base distribution representing standard traffic behavior. By assigning learned probabilities to environmental states and agent behaviors, our risk-based framework considers performance of the AV policy under a data-driven model of the world. A fundamental tradeoff emerges when comparing the requirements of our risk-based framework to other testing paradigms. Real-world testing endangers the public but is still in some sense a gold standard. Verified subsystems provide evidence that the AV should drive safely in all specified scenarios; they are limited by computational intractability and require both white-box models and a complete specifications for assigning blame (e.g. BID22 ). In turn, our risk-based framework is most useful when the base distribution P 0 is accurate. Although an estimate of p γ is not informative when P 0 is misspecified, our adaptive sampling techniques still efficiently identify dangerous scenarios in this case; such dangerous scenarios are independent of potentially subjective assignments of blame. Principled techniques for building and validating the model of the environment P 0 represent an open research question.Rigorous safety evaluation of AVs necessitates benchmarks based on adaptive adversarial conditions rather than standard nominal conditions. Importantly, our framework only requires black-box access to the driving policy and simulation environment. Our approach offers significant speedups over realworld testing and allows efficient evaluation of black-box AV input/output behavior, providing a powerful tool to aid in the design of safe AVs. DISPLAYFORM0 Evaluate and sort f (X i ) in decreasing order BID5 : DISPLAYFORM1 Discard X (1) , . . . , X (δN ) and reinitialize by resampling with replacement from X (δN +1) , . . . , X (N )
Using adaptive sampling methods to accelerate rare-event probability evaluation, we estimate the probability of an accident under a base distribution governing standard traffic behavior. 
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