2015
DOI: 10.48550/arxiv.1511.06890
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Gaussian Process Planning with Lipschitz Continuous Reward Functions: Towards Unifying Bayesian Optimization, Active Learning, and Beyond

Abstract: 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 gen… Show more

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Cited by 3 publications
(15 citation statements)
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“…We model the physical phenomenon as spatially dependent continuous process with a spatial correlation structure. Such models have recently become popular due to their mathematical tractability and accuracy [26], [32], [33], [34], [35], [5]. The degree of the spatial correlation in the process increases with the decrease of the separation between two observing locations and can be accurately modelled as a Gaussian random field 1 [29], [30], [36], [37], [38].…”
Section: A Spatial Gaussian Random Fields Backgroundmentioning
confidence: 99%
“…We model the physical phenomenon as spatially dependent continuous process with a spatial correlation structure. Such models have recently become popular due to their mathematical tractability and accuracy [26], [32], [33], [34], [35], [5]. The degree of the spatial correlation in the process increases with the decrease of the separation between two observing locations and can be accurately modelled as a Gaussian random field 1 [29], [30], [36], [37], [38].…”
Section: A Spatial Gaussian Random Fields Backgroundmentioning
confidence: 99%
“…We model the physical phenomena (both monitored and energy harvesting phenomena) as spatially dependent continuous processes with a spatial correlation structure and are independent from each other. Such models have recently become popular due to their mathematical tractability and accuracy [33], [44], [45]. The degree of the spatial correlation in the process increases with the decrease of the separation between two observing locations and can be accurately modelled as a Gaussian random field 1 [3], [24], [25], [29], [31], [37].…”
Section: A Spatial Gaussian Random Fields Backgroundmentioning
confidence: 99%
“…Its proof uses Lemma 1 and is in (Ling, Low, and Jaillet 2016). The result below is a direct consequence of Theorem 1 and will be used to theoretically guarantee the performance of our proposed nonmyopic adaptive -optimal GPP policy in Section 3:…”
Section: Introductionmentioning
confidence: 99%
“…Its proof is in (Ling, Low, and Jaillet 2016). Lemma 1 will be used to prove the Lipschitz continuity of V * t in (1) later.…”
Section: Introductionmentioning
confidence: 99%
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