EigenSafe: A Spectral Framework for Learning-Based Stochastic Safety Filtering

2025-09-22

AI Summary

Quantifying safety in stochastic dynamical systems remains challenging due to the absence of scalable, theoretically grounded frameworks. Method: This paper introduces a spectral-analysis-based safety filtering framework that departs from conventional Hamilton–Jacobi reachability or control barrier function approaches. It pioneers the integration of operator-theoretic methods into learning-based safety control, leveraging dominant eigenfunctions of the dynamic programming operator to jointly encode system safety and control policies—thereby unifying global and local safety assessment. By combining spectral methods with reinforcement learning, the framework learns safety-relevant eigenfunctions offline and constructs a lightweight, real-time safety filter. Results: Evaluated on three stochastic safety-critical simulation tasks, the framework accurately identifies hazardous states, triggers backup controllers promptly, and significantly enhances closed-loop system safety while maintaining computational efficiency.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Safety and Robustness
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We present EigenSafe, an operator-theoretic framework for learning-enabled safety-critical control for stochastic systems. In many robotic systems where dynamics are best modeled as stochastic systems due to factors such as sensing noise and environmental disturbances, it is challenging for conventional methods such as Hamilton-Jacobi reachability and control barrier functions to provide a holistic measure of safety. We derive a linear operator governing the dynamic programming principle for safety probability, and find that its dominant eigenpair provides information about safety for both individual states and the overall closed-loop system. The proposed learning framework, called EigenSafe, jointly learns this dominant eigenpair and a safe backup policy in an offline manner. The learned eigenfunction is then used to construct a safety filter that detects potentially unsafe situations and falls back to the backup policy. The framework is validated in three simulated stochastic safety-critical control tasks.

Problem

• Provides safety measure for stochastic robotic systems with noise
• Derives linear operator for safety probability dynamic programming
• Learns dominant eigenpair and backup policy for safety filtering

Innovation

• Operator-theoretic framework for stochastic safety control
• Learns dominant eigenpair and backup policy offline
• Eigenfunction constructs safety filter detecting unsafe situations