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

arXiv: https://arxiv.org/abs/1511.06890 · HTML: https://mlsanity.com/paper/1511.06890/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2015.

## Built on by (most cited first, 15 of 15)

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- [Training-Free Neural Active Learning with Initialization-Robustness Guarantees](https://mlsanity.com/paper/2306.04454/) (2023)
- [Convolutional Normalizing Flows for Deep Gaussian Processes](https://mlsanity.com/paper/2104.08472/) (2021)
- [Differentiating Policies for Non-Myopic Bayesian Optimization](https://mlsanity.com/paper/2408.07812/) (2024)
- [Dynamic Information Sub-Selection for Decision Support](https://mlsanity.com/paper/2410.23423/) (2024)
- [Do-AIQ: A Design-of-Experiment Approach to Quality Evaluation of AI Mislabel Detection Algorithm](https://mlsanity.com/paper/2208.09953/) (2022)
- [Non-Myopic Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2412.08085/) (2024)
- [Neural Nonmyopic Bayesian Optimization in Dynamic Cost Settings](https://mlsanity.com/paper/2601.06505/) (2026)

## Abstract (arXiv)

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.