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This paper presents a novel nonmyopic adaptive Gaussian process planning(GPP) framework endowed with a general class of Lipschitz continuous rewardfunctions that can unify some active learning/sensing and Bayesian optimizationcriteria and offer practitioners some flexibility to specify their desiredchoices for defining new tasks/problems. In particular, it utilizes aprincipled Bayesian sequential decision problem framework for jointly andnaturally optimizing the exploration-exploitation trade-off. In general, theresulting induced GPP policy cannot be derived exactly due to an uncountableset of candidate observations. A key contribution of our work here thus lies inexploiting the Lipschitz continuity of the reward functions to solve for anonmyopic adaptive epsilon-optimal GPP (epsilon-GPP) policy. To plan in realtime, we further propose an asymptotically optimal, branch-and-bound anytimevariant of epsilon-GPP with performance guarantee. We empirically demonstratethe effectiveness of our epsilon-GPP policy and its anytime variant in Bayesianoptimization and an energy harvesting task.

Gaussian Process Planning with Lipschitz Continuous Reward Functions: Towards Unifying Bayesian Optimization, Active Learning, and Beyond