Safely Learning Controlled Stochastic Dynamics

2025-06-03

AI Summary

This work addresses safety-critical systems by studying safe learning of controlled stochastic dynamical models from discrete-time trajectory data, with rigorous guarantees that states remain within a predefined safe region throughout both training and deployment. We propose an iterative safe control set expansion method grounded in kernel-based confidence bounds. To our knowledge, this is the first approach to jointly ensure optimal safety-aware exploration and dynamic estimation without strong modeling assumptions—such as linearity or Gaussian noise. Theoretically, we establish a Sobolev-regularity-adaptive learning rate and provide end-to-end safety and convergence guarantees. Experiments demonstrate high modeling accuracy, near 100% constraint satisfaction under safety requirements, and efficient computational performance. The method exhibits strong applicability across diverse complex domains, including robotics, finance, and biomedical systems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Safety and Robustness
• Intelligent Robots: Behavior Learning & Control

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Safely learning controlled stochastic dynamics from observations
• Ensuring system trajectories stay within predefined safe regions
• Expanding safe control sets using kernel-based confidence bounds

Innovation

• Ensures safe exploration using kernel-based bounds
• Iteratively expands initial safe control set
• Provides theoretical safety and adaptive learning guarantees