论文标题
通过Graph Gaussian过程对歧管的优化
Optimization on Manifolds via Graph Gaussian Processes
论文作者
论文摘要
本文在\ emph {Gaussian流程上限body}算法中集成了多种学习技术，以优化流形的目标函数。我们的方法是由无法获得歧管的完整表示并且查询目标昂贵的应用程序的动机。我们依靠歧管样本的点云来定义目标的图形高斯过程替代模型。查询点是使用替代模型的后部分布顺序选择的，鉴于所有先前的查询。我们就查询数量和点云的大小建立了后悔的界限。几个数字示例补充了理论并说明了我们方法的性能。
This paper integrates manifold learning techniques within a \emph{Gaussian process upper confidence bound} algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.
