mlsanityData to 7 Oct 2026

Scalable Learning of Safety Guarantees for Autonomous Systems using Hamilton-Jacobi Reachability

arXiv 2101.05916 ↗First posted 15 Jan 2021cs.RO cs.LG cs.SYcited by 10

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Abstract (arXiv)

Autonomous systems like aircraft and assistive robots often operate in scenarios where guaranteeing safety is critical. Methods like Hamilton-Jacobi reachability can provide guaranteed safe sets and controllers for such systems. However, often these same scenarios have unknown or uncertain environments, system dynamics, or predictions of other agents. As the system is operating, it may learn new knowledge about these uncertainties and should therefore update its safety analysis accordingly. However, work to learn and update safety analysis is limited to small systems of about two dimensions due to the computational complexity of the analysis. In this paper we synthesize several techniques to speed up computation: decomposition, warm-starting, and adaptive grids. Using this new framework we can update safe sets by one or more orders of magnitude faster than prior work, making this technique practical for many realistic systems. We demonstrate our results on simulated 2D and 10D near-hover quadcopters operating in a windy environment.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 22 of its 36 references that are in the map. First posted on arXiv 15 Jan 2021.

Builds on

22 of 36 references.

References · 22

  1. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,635
  2. 2017Constrained Policy Optimizationcited by 928
  3. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 347
  4. 2019Control Barrier Functions: Theory and Applicationscited by 332
  5. 2018A Lyapunov-based Approach to Safe Reinforcement Learningcited by 278
  6. 2019End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Taskscited by 256
  7. 2017Hamilton-Jacobi Reachability: A Brief Overview and Recent Advancescited by 186
  8. 2017A General Safety Framework for Learning-Based Control in Uncertain Robotic Systemscited by 150
  9. 2020Learning Stable Deep Dynamics Modelscited by 110
  10. 2018The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systemscited by 87
  11. 2017Uncertainty-Aware Reinforcement Learning for Collision Avoidancecited by 86
  12. 2020Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functionscited by 61
10 more
  1. 2014Reach-Avoid Problems with Time-Varying Dynamics, Targets and Constraintscited by 41
  2. 2016Learning Model Predictive Control for iterative tasks. A Data-Driven Control Frameworkcited by 38
  3. 2018Safely Learning to Control the Constrained Linear Quadratic Regulatorcited by 31
  4. 2019An Efficient Reachability-Based Framework for Provably Safe Autonomous Navigation in Unknown Environmentscited by 18
  5. 2016Decomposition of Reachable Sets and Tubes for a Class of Nonlinear Systemscited by 16
  6. 2020Multi-Resolution A*cited by 13
  7. 2020Safe reinforcement learning for probabilistic reachability and safety specifications: A Lyapunov-based approachcited by 10
  8. 2019Reachability-Based Safety Guarantees using Efficient Initializationscited by 9
  9. 2020Excursion Search for Constrained Bayesian Optimization under a Limited Budget of Failurescited by 6
  10. 2016Exact and Efficient Hamilton-Jacobi-based Guaranteed Safety Analysis via System Decompositioncited by 2

Built on by

Cited by year

Citing papers per year: 2021: 3; 2022: 2; 2023: 2; 2024: 1; 2025: 2.

10 papers.

  1. 2021Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learningcited by 337
  2. 2023Toward General-Purpose Robots via Foundation Models: A Survey and Meta-Analysiscited by 99
  3. 2022Provably Safe Reinforcement Learning: Conceptual Analysis, Survey, and Benchmarkingcited by 31
  4. 2025Uncertainty-aware Latent Safety Filters for Avoiding Out-of-Distribution Failurescited by 30
  5. 2025Steering Dialogue Dynamics for Robustness against Multi-turn Jailbreaking Attackscited by 20
  6. 2021Safe Value Functionscited by 7
  7. 2021Formal Verification of Unknown Dynamical Systems via Gaussian Process Regressioncited by 5
  8. 2023ConBaT: Control Barrier Transformer for Safe Policy Learningcited by 2
  9. 2022Safe Control and Learning Using Generalized Action Governorcited by 0
  10. 2024Hacking Predictors Means Hacking Cars: Using Sensitivity Analysis to Identify Trajectory Prediction Vulnerabilities for Autonomous Driving Securitycited by 0