发表机构
Extreme Materials Research Center, Korea Institute of Science and Technology; Climate and Environmental Research Institute, Korea Institute of Science and Technology; Division of AI-Robotics, KIST Campus, University of Science and Technology（韩国科学技术研究院极端材料研究中心; 韩国科学技术研究院气候与环境研究所; 科学技术大学KIST校区AI机器人系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出用于计算高斯混合微分熵的高斯-埃尔米特求积法，还提出动作空间埃尔米特多项式代理模型，在雷达指向基准中其性能优于二阶泰勒代理模型。
AI 中文摘要
高斯分布被用于对信号与状态中的不确定性进行建模，而当基础分布为多模态时，高斯混合模型常被采用。与单一高斯分布不同，高斯混合模型通常没有微分熵的闭式表达式，因此需要数值近似。我们提出了一种用于计算高斯混合微分熵的高斯-埃尔米特求积法，该方法的求积阶数可控制近似的数值分辨率。我们在一维和二维高斯混合基准测试中，将该方法与泰勒近似、解析熵界及数值积分参考值进行了评估对比。针对连续动作上的重复优化问题，我们还提出了一种动作空间中的埃尔米特多项式代理模型。在雷达指向基准测试中，该代理模型的二阶形式，在每次重规划步骤仅使用9次直接目标评估的情况下，相较于基于标称动作处局部导数的二阶泰勒代理模型，实现了显著更低的代理误差和优化器遗憾，同时该埃尔米特代理模型也提升了被测基准中的指向性能。
英文摘要
Gaussian distributions are used to model uncertainty in signals and states, and Gaussian mixtures are often used when the underlying distribution is multimodal. Unlike a single Gaussian, a Gaussian mixture generally has no closed-form expression for differential entropy and therefore requires numerical approximation. We propose a Gauss--Hermite quadrature method for evaluating Gaussian mixture differential entropy. The quadrature order controls the numerical resolution of the approximation. The method is evaluated on one- and two-dimensional Gaussian mixture benchmarks against Taylor approximations, analytic entropy bounds, and numerical integration references. For repeated optimization over continuous actions, we also propose a Hermite polynomial surrogate in action space. In a radar pointing benchmark, its second-order form achieves substantially lower surrogate error and optimizer regret than a second-order Taylor surrogate based on local derivatives at the nominal action, while both methods use nine direct objective evaluations per replanning step. The Hermite surrogate also improves pointing performance in the tested benchmark.
