This paper presents a novel nonmyopic adaptive Gaussian process planning (GPP) framework endowed with a general class of Lipschitz continuous reward functions that can unify some active learning/sensing and Bayesian optimization criteria and offer practitioners some flexibility to specify their desired choices for defining new tasks/problems. In particular, it utilizes a principled Bayesian sequential decision problem framework for jointly and naturally optimizing the exploration-exploitation trade-off. In general, the resulting induced GPP policy cannot be derived exactly due to an uncountable set of candidate observations. A key contribution of our work here thus lies in exploiting the Lipschitz continuity of the reward functions to solve for a nonmyopic adaptive epsilon-optimal GPP (epsilon-GPP) policy. To plan in real time, we further propose an asymptotically optimal, branch-and-bound anytime variant of epsilon-GPP with performance guarantee. We empirically demonstrate the effectiveness of our epsilon-GPP policy and its anytime variant in Bayesian optimization and an energy harvesting task.

本文提出了一个新颖的非远见自适应高斯过程规划 (GPP) 框架，赋予了一般类的Lipschitz连续奖励函数，可以统一一些积极学习/感知和贝叶斯优化标准，并为实践者提供一些灵活性，以指定他们定义新的任务/问题所需的选项。

具有Lipschitz连续奖励函数的高斯过程规划: 走向统一贝叶斯优化，主动学习及其它领域