Autonomous systems are increasingly implemented using end-to-end learning-based controllers. Such controllers make decisions that are executed on the real system, with images as one of the primary sensing modalities. Deep neural networks form a fundamental building block of such controllers. Unfortunately, the existing neural-network verification tools do not scale to inputs with thousands of dimensions -- especially when the individual inputs (such as pixels) are devoid of clear physical meaning. This paper takes a step towards connecting exhaustive closed-loop verification with high-dimensional controllers. Our key insight is that the behavior of a high-dimensional controller can be approximated with several low-dimensional controllers. To balance the approximation accuracy and verifiability of our low-dimensional controllers, we leverage the latest verification-aware knowledge distillation. Then, we inflate low-dimensional reachability results with statistical approximation errors, yielding a high-confidence reachability guarantee for the high-dimensional controller. We investigate two inflation techniques -- based on trajectories and control actions -- both of which show convincing performance in three OpenAI gym benchmarks.

翻译：自主系统日益采用基于端到端学习型控制器实现。此类控制器在真实系统上执行决策时，图像作为主要传感模态之一。深度神经网络构成这类控制器的核心构建模块。然而，现有神经网络验证工具难以扩展至数千维度的输入——尤其当个体输入（如像素）缺乏明确物理意义时。本文旨在连接穷举式闭环验证与高维控制器。我们的核心洞察在于：高维控制器的行为可通过多个低维控制器近似。为平衡低维控制器的近似精度与可验证性，我们借鉴了最新的验证感知知识蒸馏技术。随后，通过统计近似误差对低维可达性结果进行膨胀处理，从而为高维控制器提供高置信度的可达性保证。我们研究了两种基于轨迹和控制动作的膨胀技术，在三个OpenAI Gym基准测试中均展现出令人信服的效果。