📄 中文摘要
哈密顿-雅可比-贝尔曼方程在强化学习和扩散模型中具有重要应用。强化学习通过与环境的交互来优化决策过程，而扩散模型则用于生成样本和建模复杂的概率分布。两者结合能够提升智能体在复杂环境中的表现。研究表明，利用哈密顿-雅可比-贝尔曼方程，可以有效地解决强化学习中的价值函数问题，并为扩散模型提供更强的理论基础。这种方法不仅提高了学习效率，还在多种任务中展现出优越的性能，推动了智能体在动态环境中的适应能力和决策质量的提升。
哈密顿-雅可比-贝尔曼方程：强化学习与扩散模型
📄 English Summary
Hamilton-Jacobi-Bellman Equation: Reinforcement Learning and Diffusion Models
The Hamilton-Jacobi-Bellman (HJB) equation plays a crucial role in both reinforcement learning and diffusion models. Reinforcement learning optimizes decision-making through interaction with the environment, while diffusion models are utilized for sample generation and modeling complex probability distributions. The integration of these two approaches enhances the performance of agents in complex environments. Research indicates that leveraging the HJB equation effectively addresses the value function problem in reinforcement learning and provides a robust theoretical foundation for diffusion models. This methodology not only improves learning efficiency but also demonstrates superior performance across various tasks, advancing the adaptability and decision quality of agents in dynamic settings.