论文标题
滴水：域的细化迭代及其多型的域，用于落后可及性分析神经反馈回路
DRIP: Domain Refinement Iteration with Polytopes for Backward Reachability Analysis of Neural Feedback Loops
论文作者
论文摘要
数据驱动控制技术的安全认证仍然是一个主要的开放问题。这项工作调查了向后的可及性，作为为由神经网络（NN）政策控制的系统提供避免碰撞保证的框架。由于NN通常不可逆转，因此现有方法保守地假设了一个放宽NN的域，这会导致一组可能导致系统进入障碍物的状态的过度关注（即，反射（BP）集）。为了解决这个问题，我们介绍了滴水，这是一种在放松域上具有细化循环的算法，从而实质上会收紧BP集合边界。此外，我们引入了一种公式，该公式可以直接获得多面体的闭合形式表示，以限制BP设置比先前的工作更紧密，该工作需要求解线性程序并使用超矩形。此外，这项工作扩展了NN松弛算法以处理多层域，从而进一步收紧了BP集合的边界。在控制系统的数值实验中证明了滴水，包括由学习的NN障碍避免政策控制的地面机器人。
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.
