用谱方法评估学习系统安全概率，提升机器人决策可靠性。
EigenSafe: A Spectral Framework for Learning-Based Probabilistic Safety Assessment
- 基于算子理论构建安全评估框架，提取主导特征对
- 学习到的特征对可精准反映状态-动作对的安全概率
- 适用于强化学习与模仿学习，适合机器人安全控制场景
我们提出EigenSafe，一种基于算子理论的学习型随机系统的安全评估框架。在诸多机器人应用中，系统动态因感知噪声和环境扰动呈现固有随机性，传统方法如哈密顿-雅可比可达性分析与控制屏障函数难以提供与实际安全概率精确匹配的安全评判。本文推导出支配安全概率动态规划原理的线性算子，并发现其主导特征对能同时为单个状态-动作对及整个闭环系统提供关键安全信息。所提框架通过学习该主导特征对，可用于指导或约束策略更新。实验表明，学习到的特征对有效促进安全强化学习；进一步在UR3机械臂食品准备任务中，通过机器人操作实验验证了其提升模仿学习所得策略安全性的可行性。
原文摘要 · Abstract (English)
We present EigenSafe, an operator-theoretic framework for safety assessment of learning-enabled stochastic systems. In many robotic applications, the dynamics are inherently stochastic due to factors such as sensing noise and environmental disturbances, and it is challenging for conventional methods such as Hamilton-Jacobi reachability and control barrier functions to provide a well-calibrated safety critic that is tied to the actual safety probability. We derive a linear operator that governs the dynamic programming principle for safety probability, and find that its dominant eigenpair provides critical safety information for both individual state-action pairs and the overall closed-loop system. The proposed framework learns this dominant eigenpair, which can be used to either inform or constrain policy updates. We demonstrate that the learned eigenpair effectively facilitates safe reinforcement learning. Further, we validate its applicability in enhancing the safety of learned policies from imitation learning through robot manipulation experiments using a UR3 robotic arm in a food preparation task.
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