Gradient-Free Neural Hamilton-Jacobi Reachability for Scalable Safety-Critical Control

• URL: http://arxiv.org/abs/2609.14087v1
• Date: Sat, 12 Sep 2026 18:03:51 GMT
• Title: Gradient-Free Neural Hamilton-Jacobi Reachability for Scalable Safety-Critical Control
• Abstract summary: Hamilton-Jacobi (HJ) reachability provides a principled framework for synthesizing safety certificates and robust controllers for safety-critical robotic systems.<n>Applying reachability analysis to high-dimensional nonlinear systems remains challenging.<n>We propose a discrete-time neural reachability framework for control-disturbance-affine systems.
• Score: 6.387263468033964
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Hamilton-Jacobi (HJ) reachability provides a principled framework for synthesizing safety certificates and robust controllers for safety-critical robotic systems. However, applying reachability analysis to high-dimensional nonlinear systems remains challenging: classical grid-based solvers suffer from the curse of dimensionality, continuous-time neural solvers require accurate spatial value gradients, and reinforcement-learning-based approaches often suffer from weak boundary anchoring and non-stationary adversarial policy optimization. We propose a discrete-time neural reachability framework for control-disturbance-affine systems that learns backward reachable tubes (BRTs) and backward reach-avoid tubes (BRATs) through Bellman-Isaacs value propagation. Our key idea is to combine equation-driven self-supervision with structured policy learning: rather than computing explicit PDE-gradients, we exploit the bang-bang structure of optimal safety interventions to construct approximate teacher actions from gradient-free value probes, converting adversarial actor learning into supervised policy learning. To stabilize long-horizon value propagation, we leverage the learned actor to train the value function backward from the terminal boundary using a windowed temporal curriculum, where each window is used as the boundary condition for the next window. Across benchmark problems up to 80 dimensions, our method learns accurate reachability value functions while improving stability over existing learning-based solvers. We further demonstrate observation-space scalability on F1-tenth racing with over 16,000-dimensional egocentric inputs. The learned safety filter generalizes zero-shot to unseen tracks and transfers to a physical RC car, achieving real-time robust collision avoidance.

Related papers

• Kernel-Based Learning of Safety Barriers [0.9367224590861915]
  Rapid integration of AI algorithms in safety-critical applications is raising concerns about the ability to meet stringent safety standards.<n>Traditional tools for formal safety verification struggle with the black-box nature of AI-driven systems.<n>We present a data-driven approach for safety verification and synthesis of black-box systems with discrete-time dynamics.
  arXiv  Detail & Related papers  (2026-01-17T10:42:35Z)
• Foundations of Safe Online Reinforcement Learning in the Linear Quadratic Regulator: $\sqrt{T}$-Regret [5.108909395876561]
  We prove rigorous regret bounds for safety-constrained reinforcement learning.<n>We provide the first safe algorithm that achieves regret of $tildeO_T(sqrtT)$.
  arXiv  Detail & Related papers  (2025-04-25T19:22:57Z)
• Integrating DeepRL with Robust Low-Level Control in Robotic Manipulators for Non-Repetitive Reaching Tasks [0.24578723416255746]
  In robotics, contemporary strategies are learning-based, characterized by a complex black-box nature and a lack of interpretability. We propose integrating a collision-free trajectory planner based on deep reinforcement learning (DRL) with a novel auto-tuning low-level control strategy.
  arXiv  Detail & Related papers  (2024-02-04T15:54:03Z)
• A Multiplicative Value Function for Safe and Efficient Reinforcement Learning [131.96501469927733]
  We propose a safe model-free RL algorithm with a novel multiplicative value function consisting of a safety critic and a reward critic. The safety critic predicts the probability of constraint violation and discounts the reward critic that only estimates constraint-free returns. We evaluate our method in four safety-focused environments, including classical RL benchmarks augmented with safety constraints and robot navigation tasks with images and raw Lidar scans as observations.
  arXiv  Detail & Related papers  (2023-03-07T18:29:15Z)
• Evaluating Model-free Reinforcement Learning toward Safety-critical Tasks [70.76757529955577]
  This paper revisits prior work in this scope from the perspective of state-wise safe RL. We propose Unrolling Safety Layer (USL), a joint method that combines safety optimization and safety projection. To facilitate further research in this area, we reproduce related algorithms in a unified pipeline and incorporate them into SafeRL-Kit.
  arXiv  Detail & Related papers  (2022-12-12T06:30:17Z)
• Log Barriers for Safe Black-box Optimization with Application to Safe Reinforcement Learning [72.97229770329214]
  We introduce a general approach for seeking high dimensional non-linear optimization problems in which maintaining safety during learning is crucial. Our approach called LBSGD is based on applying a logarithmic barrier approximation with a carefully chosen step size. We demonstrate the effectiveness of our approach on minimizing violation in policy tasks in safe reinforcement learning.
  arXiv  Detail & Related papers  (2022-07-21T11:14:47Z)
• Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learning [24.56889192688925]
  Reach-avoid optimal control problems are central to safety and liveness assurance for autonomous robotic systems. Recent successes in reinforcement learning methods to approximately solve optimal control problems with performance objectives make their application to certification problems attractive. Recent work has shown promise in extending the reinforcement learning machinery to handle safety-type problems, whose objective is not a sum, but a minimum (or maximum) over time.
  arXiv  Detail & Related papers  (2021-12-23T00:44:38Z)
• Closing the Closed-Loop Distribution Shift in Safe Imitation Learning [80.05727171757454]
  We treat safe optimization-based control strategies as experts in an imitation learning problem. We train a learned policy that can be cheaply evaluated at run-time and that provably satisfies the same safety guarantees as the expert.
  arXiv  Detail & Related papers  (2021-02-18T05:11:41Z)
• Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems [81.7983463275447]
  Learning-based control algorithms require data collection with abundant supervision for training. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained optimal control with dynamics learning and feedback control.
  arXiv  Detail & Related papers  (2020-05-09T05:57:43Z)
• Learning Control Barrier Functions from Expert Demonstrations [69.23675822701357]
  We propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs) We analyze an optimization-based approach to learning a CBF that enjoys provable safety guarantees under suitable Lipschitz assumptions on the underlying dynamical system. To the best of our knowledge, these are the first results that learn provably safe control barrier functions from data.
  arXiv  Detail & Related papers  (2020-04-07T12:29:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.