Bridging Dimensions: Confident Reachability for High-Dimensional Controllers

• URL: http://arxiv.org/abs/2311.04843v4
• Date: Thu, 2 May 2024 15:33:36 GMT
• Title: Bridging Dimensions: Confident Reachability for High-Dimensional Controllers
• Authors: Yuang Geng, Jake Brandon Baldauf, Souradeep Dutta, Chao Huang, Ivan Ruchkin,
• Abstract summary: 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. Then, we inflate low-dimensional reachability results with statistical approximation errors, yielding a high-confidence reachability guarantee for the high-dimensional controller.
• Score: 3.202200341692044
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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