标题： 基于策略迭代的探索性哈密顿-雅可比-贝尔曼方程的物理信息方法 显示英文标题

标题： Physics-informed approach for exploratory Hamilton--Jacobi--Bellman equations via policy iterations

摘要： 我们提出了一种基于物理信息神经网络（PINNs）的无网格策略迭代框架，用于求解熵正则化随机控制问题。 该方法通过自动微分和神经近似，迭代地在软策略评估和改进之间交替进行，而无需依赖空间离散化。 我们提出了一个详细的$L^2$误差分析，将总近似误差分解为三个来源：迭代误差、策略网络误差和PDE残差误差。 所提出的算法通过一系列具有挑战性的控制任务进行了验证，包括5D和10D的高维线性二次调节问题，以及摆锤和小车杆问题等非线性系统。 数值结果证实了我们的方法在各种线性和非线性基准测试中的可扩展性、准确性和鲁棒性。 显示英文摘要

摘要： We propose a mesh-free policy iteration framework based on physics-informed neural networks (PINNs) for solving entropy-regularized stochastic control problems. The method iteratively alternates between soft policy evaluation and improvement using automatic differentiation and neural approximation, without relying on spatial discretization. We present a detailed $L^2$ error analysis that decomposes the total approximation error into three sources: iteration error, policy network error, and PDE residual error. The proposed algorithm is validated with a range of challenging control tasks, including high-dimensional linear-quadratic regulation in 5D and 10D, as well as nonlinear systems such as pendulum and cartpole problems. Numerical results confirm the scalability, accuracy, and robustness of our approach across both linear and nonlinear benchmarks.