# SABLAS: Learning Safe Control for Black-box Dynamical Systems

arXiv: https://arxiv.org/abs/2201.01918 · HTML: https://mlsanity.com/paper/2201.01918/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 6 Jan 2022.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Projection-Based Constrained Policy Optimization](https://mlsanity.com/paper/2010.03152/) (2020)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Backpropagation through the Void: Optimizing control variates for black-box gradient estimation](https://mlsanity.com/paper/1711.00123/) (2017)
- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [KETO: Learning Keypoint Representations for Tool Manipulation](https://mlsanity.com/paper/1910.11977/) (2019)
- [Lyapunov-stable neural-network control](https://mlsanity.com/paper/2109.14152/) (2021)
- [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021)
- [Learning Certified Control using Contraction Metric](https://mlsanity.com/paper/2011.12569/) (2020)
- [Black-Box Control for Linear Dynamical Systems](https://mlsanity.com/paper/2007.06650/) (2020)
- [Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design](https://mlsanity.com/paper/1503.03144/) (2015)
- [Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functions](https://mlsanity.com/paper/2010.16001/) (2020)
- [Density Constrained Reinforcement Learning](https://mlsanity.com/paper/2106.12764/) (2021)
- [Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approach](https://mlsanity.com/paper/2006.04361/) (2020)
- [MADER: Trajectory Planner in Multi-Agent and Dynamic Environments](https://mlsanity.com/paper/2010.11061/) (2020)
- [Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertainties](https://mlsanity.com/paper/2004.05273/) (2020)
- [Learning Control Lyapunov Functions from Counterexamples and Demonstrations](https://mlsanity.com/paper/1804.05285/) (2018)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [FASTER: Fast and Safe Trajectory Planner for Flights in Unknown Environments](https://mlsanity.com/paper/1903.03558/) (2019)
- [On-The-Fly Control of Unknown Smooth Systems from Limited Data](https://mlsanity.com/paper/2009.12733/) (2020)
- [FISAR: Forward Invariant Safe Reinforcement Learning with a Deep Neural Network-Based Optimize](https://mlsanity.com/paper/2006.11419/) (2020)

## Built on by (most cited first, 17 of 17)

- [In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution States](https://mlsanity.com/paper/2301.12012/) (2023)
- [Dynamic Model Predictive Shielding for Provably Safe Reinforcement Learning](https://mlsanity.com/paper/2405.13863/) (2024)
- [Value Functions are Control Barrier Functions: Verification of Safe Policies using Control Theory](https://mlsanity.com/paper/2306.04026/) (2023)
- [Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizon](https://mlsanity.com/paper/2309.11453/) (2023)
- [RAIL: Reachability-Aided Imitation Learning for Safe Policy Execution](https://mlsanity.com/paper/2409.19190/) (2024)
- [How Does the Lagrangian Guide Safe Reinforcement Learning through Diffusion Models?](https://mlsanity.com/paper/2602.02924/) (2026)
- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (2024)
- [ConBaT: Control Barrier Transformer for Safe Policy Learning](https://mlsanity.com/paper/2303.04212/) (2023)
- [Neural Control and Certificate Repair via Runtime Monitoring](https://mlsanity.com/paper/2412.12996/) (2024)
- [Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions](https://mlsanity.com/paper/2208.10733/) (2022)
- [Safety Certification in the Latent space using Control Barrier Functions and World Models](https://mlsanity.com/paper/2507.13871/) (2025)
- [Domain Adaptive Safety Filters via Deep Operator Learning](https://mlsanity.com/paper/2410.14528/) (2024)
- [Pre-Trained Vision Models as Perception Backbones for Safety Filters in Autonomous Driving](https://mlsanity.com/paper/2410.22585/) (2024)
- [Learning Neural Control Barrier Functions from Expert Demonstrations using Inverse Constraint Learning](https://mlsanity.com/paper/2510.21560/) (2025)
- [Fulfilling Formal Specifications ASAP by Model-free Reinforcement Learning](https://mlsanity.com/paper/2304.12508/) (2023)
- [An Intelligent Social Learning-based Optimization Strategy for Black-box Robotic Control with Reinforcement Learning](https://mlsanity.com/paper/2311.06576/) (2023)
- [Safe Score Matching: Diffusion Policies with Hamilton-Jacobi Reachability for Online Safe Reinforcement Learning](https://mlsanity.com/paper/2609.33337/) (2026)

## Abstract (arXiv)

Control certificates based on barrier functions have been a powerful tool to generate probably safe control policies for dynamical systems. However, existing methods based on barrier certificates are normally for white-box systems with differentiable dynamics, which makes them inapplicable to many practical applications where the system is a black-box and cannot be accurately modeled. On the other side, model-free reinforcement learning (RL) methods for black-box systems suffer from lack of safety guarantees and low sampling efficiency. In this paper, we propose a novel method that can learn safe control policies and barrier certificates for black-box dynamical systems, without requiring for an accurate system model. Our method re-designs the loss function to back-propagate gradient to the control policy even when the black-box dynamical system is non-differentiable, and we show that the safety certificates hold on the black-box system. Empirical results in simulation show that our method can significantly improve the performance of the learned policies by achieving nearly 100% safety and goal reaching rates using much fewer training samples, compared to state-of-the-art black-box safe control methods. Our learned agents can also generalize to unseen scenarios while keeping the original performance. The source code can be found at https://github.com/Zengyi-Qin/bcbf.