DRIP: Domain Refinement Iteration with Polytopes for Backward Reachability Analysis of Neural Feedback Loops

• Main Authors: Everett, Michael, Bunel, Rudy, Omidshafiei, Shayegan
• Format: Journal Article
• Language: English
• Published: 08.12.2022
• Subjects: Computer Science - Learning; Computer Science - Systems and Control
• DOI: 10.48550/arxiv.2212.04646

Safety certification of data-driven control techniques remains a major open problem. This work investigates backward reachability as a framework for providing collision avoidance guarantees for systems controlled by neural network (NN) policies. Because NNs are typically not invertible, existing methods conservatively assume a domain over which to relax the NN, which causes loose over-approximations of the set of states that could lead the system into the obstacle (i.e., backprojection (BP) sets). To address this issue, we introduce DRIP, an algorithm with a refinement loop on the relaxation domain, which substantially tightens the BP set bounds. Furthermore, we introduce a formulation that enables directly obtaining closed-form representations of polytopes to bound the BP sets tighter than prior work, which required solving linear programs and using hyper-rectangles. Furthermore, this work extends the NN relaxation algorithm to handle polytope domains, which further tightens the bounds on BP sets. DRIP is demonstrated in numerical experiments on control systems, including a ground robot controlled by a learned NN obstacle avoidance policy.