Bridging Dimensions: Confident Reachability for High-Dimensional Controllers

TL;DR

This paper introduces a method to verify high-dimensional neural network controllers by approximating them with low-dimensional controllers, using knowledge distillation and statistical inflation to provide high-confidence reachability guarantees.

Contribution

It presents a novel approach to connect high-dimensional controller verification with low-dimensional approximations using verification-aware knowledge distillation.

Findings

Effective in three OpenAI gym benchmarks

Provides high-confidence reachability guarantees

Balances approximation accuracy and verifiability

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.