aiqbench analysis
ConDR addresses critical safety verification in high-dimensional dynamical systems by introducing a one-sided loss function that guarantees the learned unsafe set contains all true failure states. This method overcomes the scalability limits of classical grid solvers while eliminating the false-negative risks inherent in previous neural approaches like DeepReach. The technique is particularly relevant for autonomous robotics and control systems where worst-case disturbance analysis is mandatory.
ConDR: Conservative Reachability through Neural Hamilton-Jacobi Subsolutions
arXiv:2611.06802v1 Announce Type: new Abstract: Hamilton-Jacobi (HJ) Reachability identifies the unsafe states of a dynamical system from which it can be forced into failure under worst-case disturbance. However, classical grid-based solvers scale exponentially with state dimension. DeepReach improves scalability by replacing the grid with a neural value function trained on the HJ-Isaacs (HJI) variational inequality (VI), but penalizes both sides of the residual equally. This allows the learned value to lie above the true one and unsafe states to be misclassified as safe. We propose Conservative DeepReach (ConDR) which aims to learn a subsolution of the HJI VI such that the learned unsafe set contains the true one. ConDR enforces the obstacle branch and terminal condition by construction, pushes the HJI residual to a safety margin $\epsilon$ below zero with a one-sided loss, and prevents the degenerate solution of classifying everything as unsafe. We prove that the exact solution of the margin-shifted VI that ConDR trains toward is a subsolution of the original VI so its unsafe set contains the true one and its value lies within $\epsilon\tau$ of the true value function. We compare against DeepReach and MADR in the established systems of Air3D, Air6D, a 9D multi-vehicle system, and a 13D quadrotor. ConDR reports the lowest rate of unsafe state misclassified and the lowest closed-loop collision rates with at most a small increase in intervention. On Air3D and Air6D, ConDR tolerates model mismatch that scales with $\epsilon$. At matched false-negative rates, ConDR's unsafe sets are smaller than the baselines showing the safety is not obtained by trivial over-approximation.
Abstract:Hamilton-Jacobi (HJ) Reachability identifies the unsafe states of a dynamical system from which it can be forced into failure under worst-case disturbance. However, classical grid-based solvers scale exponentially with state dimension. DeepReach improves scalability by replacing the grid with a neural value function trained on the HJ-Isaacs (HJI) variational inequality (VI), but penalizes both sides of the residual equally. This allows the learned value to lie above the true one and unsafe states to be misclassified as safe. We propose Conservative DeepReach (ConDR) which aims to learn a subsolution of the HJI VI such that the learned unsafe set contains the true one. ConDR enforces the obstacle branch and terminal condition by construction, pushes the HJI residual to a safety margin $\epsilon$ below zero with a one-sided loss, and prevents the degenerate solution of classifying everything as unsafe. We prove that the exact solution of the margin-shifted VI that ConDR trains toward is a subsolution of the original VI so its unsafe set contains the true one and its value lies within $\epsilon\tau$ of the true value function. We compare against DeepReach and MADR in the established systems of Air3D, Air6D, a 9D multi-vehicle system, and a 13D quadrotor. ConDR reports the lowest rate of unsafe state misclassified and the lowest closed-loop collision rates with at most a small increase in intervention. On Air3D and Air6D, ConDR tolerates model mismatch that scales with $\epsilon$. At matched false-negative rates, ConDR's unsafe sets are smaller than the baselines showing the safety is not obtained by trivial over-approximation.
Robotics (cs.RO); Machine Learning (cs.LG); Systems and Control (eess.SY)
arXiv:2611.06802 [cs.RO]
(or arXiv:2611.06802v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2611.06802 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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