强化学习中的Hamilton-Jacobi可达性：综述
Hamilton-Jacobi Reachability in Reinforcement Learning: A Survey
AI总结：
本文综述了强化学习中Hamilton-Jacobi可达性估计的最新进展，探讨了如何通过同步计算可达性值函数与学习控制策略来克服高维系统的计算复杂度限制，从而提升策略的安全性与性能。
摘要：
近期文献提出了一些方法，这些方法在学习高性能控制策略的同时保持安全性保证。合成Hamilton-Jacobi (HJ) 可达集已成为验证安全性和监督复杂、高维系统基于强化学习的控制策略训练的有效工具。此前，HJ可达性仅限于验证低维动力系统，主要是因为其依赖的动态规划方法的计算复杂度随系统状态数量呈指数级增长。近年来，大量提出的方法解决了这一局限性，它们在学习控制策略的同时计算可达性值函数，从而在扩展HJ可达性分析的同时，仍能对真实可达集保持可靠的估计。这些HJ可达性近似被用于提高所学控制策略的安全性，甚至提升奖励性能，并且能够解决具有动态障碍物和/或基于激光雷达或视觉观测的挑战性任务。在这篇综述论文中，我们回顾了强化学习中HJ可达性估计领域的最新进展，这将为进一步研究高维系统的可靠性提供基础。
英文摘要：
Recent literature has proposed approaches that learn control policies with high performance while maintaining safety guarantees. Synthesizing Hamilton-Jacobi (HJ) reachable sets has become an effective tool for verifying safety and supervising the training of reinforcement learning-based control policies for complex, high-dimensional systems. Previously, HJ reachability was restricted to verifying low-dimensional dynamical systems primarily because the computational complexity of the dynamic programming approach it relied on grows exponentially with the number of system states. In recent years, a litany of proposed methods addresses this limitation by computing the reachability value function simultaneously with learning control policies to scale HJ reachability analysis while still maintaining a reliable estimate of the true reachable set. These HJ reachability approximations are used to improve the safety, and even reward performance, of learned control policies and can solve challenging tasks such as those with dynamic obstacles and/or with lidar-based or vision-based observations. In this survey paper, we review the recent developments in the field of HJ reachability estimation in reinforcement learning that would provide a foundational basis for further research into reliability in high-dimensional systems.
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