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.

翻译：本文将多种学习技巧整合到 \ emph{ Gausian 进程上限信任约束值 算法中, 以优化一个多功能上的客观功能。 我们的方法是由无法完全代表多元的应用程序驱动的, 询问目标费用昂贵。 我们依靠多个样本的点云来定义一个用于目标的Gaussian 进程替代模型。 使用所有先前查询的替代模型的后方分布顺序选择 。 我们根据查询次数和点云的大小确定了遗憾界限。 几个数字例子补充了该理论,并展示了我们方法的性能 。