A particularly challenging problem in AI safety is providing guarantees on the behavior of high-dimensional autonomous systems. Verification approaches centered around reachability analysis fail to scale, and purely statistical approaches are constrained by the distributional assumptions about the sampling process. Instead, we pose a distributionally robust version of the statistical verification problem for black-box systems, where our performance guarantees hold over a large family of distributions. This paper proposes a novel approach based on uncertainty quantification using concepts from imprecise probabilities. A central piece of our approach is an ensemble technique called Imprecise Neural Networks, which provides the uncertainty quantification. Additionally, we solve the allied problem of exploring the input set using active learning. The active learning uses an exhaustive neural-network verification tool Sherlock to collect samples. An evaluation on multiple physical simulators in the openAI gym Mujoco environments with reinforcement-learned controllers demonstrates that our approach can provide useful and scalable guarantees for high-dimensional systems.

Conformal prediction is a statistical tool for producing prediction regions of machine learning models that are valid with high probability. However, applying conformal prediction to time series data leads to conservative prediction regions. In fact, to obtain prediction regions over T time steps with confidence 1--delta, previous works require that each individual prediction region is valid with confidence 1--delta/T. We propose an optimization-based method for reducing this conservatism to enable long horizon planning and verification when using learning-enabled time series predictors. Instead of considering prediction errors individually at each time step, we consider a parameterized prediction error over multiple time steps. By optimizing the parameters over an additional dataset, we find prediction regions that are not conservative. We show that this problem can be cast as a mixed integer linear complementarity program (MILCP), which we then relax into a linear complementarity program (LCP). Additionally, we prove that the relaxed LP has the same optimal cost as the original MILCP. Finally, we demonstrate the efficacy of our method on case studies using pedestrian trajectory predictors and F16 fighter jet altitude predictors.

This paper addresses a safe planning and control problem for mobile robots operating in communication- and sensor-limited dynamic environments. In this case the robots cannot sense the objects around them and must instead rely on intermittent, external information about the environment, as e.g., in underwater applications. The challenge in this case is that the robots must plan using only this stale data, while accounting for any noise in the data or uncertainty in the environment. To address this challenge we propose a compositional technique which leverages neural networks to quickly plan and control a robot through crowded and dynamic environments using only intermittent information. Specifically, our tool uses reachability analysis and potential fields to train a neural network that is capable of generating safe control actions. We demonstrate our technique both in simulation with an underwater vehicle crossing a crowded shipping channel and with real experiments with ground vehicles in communication-and sensor-limited environments.