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

• URL: http://arxiv.org/abs/2212.04646v1
• Date: Fri, 9 Dec 2022 03:06:58 GMT
• Title: DRIP: Domain Refinement Iteration with Polytopes for Backward Reachability Analysis of Neural Feedback Loops
• Authors: Michael Everett, Rudy Bunel, Shayegan Omidshafiei
• Abstract summary: 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 assume a domain over which to relax the NN, which causes loose over-approximations of the set of states. We introduce DRIP, an algorithm with a refinement loop on the relaxation domain, which substantially tightens the BP set bounds.
• Score: 12.706980346861986
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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