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：本文将流形学习技术集成到*高斯过程上置信界*算法中，用于优化流形上的目标函数。我们的方法源于以下应用场景：无法获取流形的完整表示，且目标函数的查询代价高昂。我们利用流形样本点云定义目标函数的图高斯过程代理模型，基于该代理模型在给定所有历史查询结果下的后验分布，顺序选取新的查询点。我们建立了与查询次数及点云规模相关的遗憾界。若干数值算例对理论进行补充，并展示了我们方法的性能。