Deep Galerkin 反馈律下基于智能体动力学的最优控制
Optimal Control of Agent-Based Dynamics under Deep Galerkin Feedback Laws
AI总结：
针对 Deep Galerkin Method 在高维平均场控制中的采样与高方差策略近似问题，提出基于漂移松弛的采样方法，并在意见动力学和 LQR 任务中验证其成本与性能优势。
摘要：
自动态规划概念提出以来，最困难的挑战之一便是充分处理高维控制问题。随着维度增加，深度神经网络的应用有望规避原本呈指数增长的复杂性问题。本文专门研究 Deep Galerkin Method 所面临的采样问题，提出一种基于漂移松弛的采样方法，以缓解高方差策略近似的症状。该方法在平均场控制问题上得到验证，即 Sznajd 模型与 Hegselmann-Krause 模型所呈现的意见动力学变体。所得策略相较人工优化的控制函数带来显著成本降低，并在线性二次调节器问题上相较 Deep FBSDE 方法表现出改进。
英文摘要：
Ever since the concepts of dynamic programming were introduced, one of the most difficult challenges has been to adequately address high-dimensional control problems. With growing dimensionality, the utilisation of Deep Neural Networks promises to circumvent the issue of an otherwise exponentially increasing complexity. The paper specifically investigates the sampling issues the Deep Galerkin Method is subjected to. It proposes a drift relaxation-based sampling approach to alleviate the symptoms of high-variance policy approximations. This is validated on mean-field control problems; namely, the variations of the opinion dynamics presented by the Sznajd and the Hegselmann-Krause model. The resulting policies induce a significant cost reduction over manually optimised control functions and show improvements on the Linear-Quadratic Regulator problem over the Deep FBSDE approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
