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Safely Learning Controlled Stochastic Dynamics

arXiv 2506.02754 ↗First posted 3 Jun 2025stat.ML cs.LGcited by 0

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Abstract (arXiv)

We address the problem of safely learning controlled stochastic dynamics from discrete-time trajectory observations, ensuring system trajectories remain within predefined safe regions during both training and deployment. Safety-critical constraints of this kind are crucial in applications such as autonomous robotics, finance, and biomedicine. We introduce a method that ensures safe exploration and efficient estimation of system dynamics by iteratively expanding an initial known safe control set using kernel-based confidence bounds. After training, the learned model enables predictions of the system's dynamics and permits safety verification of any given control. Our approach requires only mild smoothness assumptions and access to an initial safe control set, enabling broad applicability to complex real-world systems. We provide theoretical guarantees for safety and derive adaptive learning rates that improve with increasing Sobolev regularity of the true dynamics. Experimental evaluations demonstrate the practical effectiveness of our method in terms of safety, estimation accuracy, and computational efficiency.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 37 of its 63 references that are in the map. First posted on arXiv 3 Jun 2025.

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References · 37

  1. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 366
  2. 2018Multi-Goal Reinforcement Learning: Challenging Robotics Environments and Request for Researchcited by 260
  3. 2018Safe Exploration in Continuous Action Spacescited by 247
  4. 2022A Review of Safe Reinforcement Learning: Methods, Theory and Applicationscited by 181
  5. 2013Finite-Time Analysis of Kernelised Contextual Banditscited by 177
  6. 2017A General Safety Framework for Learning-Based Control in Uncertain Robotic Systemscited by 163
  7. 2020On Information Gain and Regret Bounds in Gaussian Process Banditscited by 158
  8. 2018Learning-based Model Predictive Control for Safe Explorationcited by 120
  9. 2022Safe Planning in Dynamic Environments using Conformal Predictioncited by 119
  10. 2018A predictive safety filter for learning-based control of constrained nonlinear dynamical systemscited by 118
  11. 2020Safe Reinforcement Learning in Constrained Markov Decision Processescited by 115
  12. 2018The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systemscited by 88
25 more
  1. 2020Active Learning for Nonlinear System Identification with Guaranteescited by 80
  2. 2018Stagewise Safe Bayesian Optimization with Gaussian Processescited by 79
  3. 2016Safe Exploration in Finite Markov Decision Processes with Gaussian Processescited by 75
  4. 2018Statistical Optimality of Stochastic Gradient Descent on Hard Learning Problems through Multiple Passescited by 69
  5. 2018Deep Dynamical Modeling and Control of Unsteady Fluid Flowscited by 68
  6. 2019Safe Exploration for Interactive Machine Learningcited by 51
  7. 2021Safe Reinforcement Learning Using Advantage-Based Interventioncited by 47
  8. 2020Bandit optimisation of functions in the Mat'ern kernel RKHScited by 40
  9. 2014Safe Exploration of State and Action Spaces in Reinforcement Learningcited by 38
  10. 2018Linear model predictive safety certification for learning-based controlcited by 37
  11. 2020Causal models for dynamical systemscited by 34
  12. 2022Safe Reinforcement Learning Using Black-Box Reachability Analysiscited by 26
  13. 2020Safe Active Dynamics Learning and Control: A Sequential Exploration-Exploitation Frameworkcited by 19
  14. 2022GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systemscited by 17
  15. 2024DiffPhyCon: A Generative Approach to Control Complex Physical Systemscited by 17
  16. 2019Probabilistic Safety Constraints for Learned High Relative Degree System Dynamicscited by 9
  17. 2022Information-Theoretic Safe Exploration with Gaussian Processescited by 9
  18. 2024Safe Guaranteed Exploration for Non-linear Systemscited by 8
  19. 2020Safely Learning Dynamical Systems from Short Trajectoriescited by 5
  20. 2020Sequential Convex Programming For Non-Linear Stochastic Optimal Controlcited by 4
  21. 2023Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergencecited by 4
  22. 2023Risk-Averse Trajectory Optimization via Sample Average Approximationcited by 4
  23. 2024Safe Time-Varying Optimization based on Gaussian Processes with Spatio-Temporal Kernelcited by 4
  24. 2022First-Order Pontryagin Maximum Principle for Risk-Averse Stochastic Optimal Control Problemscited by 3
  25. 2022Sample Average Approximation for Stochastic Programming with Equality Constraintscited by 3

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