Gaussian Process Planning with Lipschitz Continuous Reward Functions
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Jaillet_Gaussian process planning.pdf
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512.87 KB
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Author(s)
Ling, Chun Kai
Low, Kian Hsiang
Jaillet, Patrick
Date Issued
February 2016
Journal
Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, AAAI'16
Publisher
Association for Computing Machinery
Citation
Ling, Chun Kai, Kian Hsiang Low and Patrick Jaillet. "Gaussian process planning with lipschitz continuous reward functions: towards unifying Bayesian optimization, active learning, and beyond." Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence AAAI'16, 12-17 February, 2016, Phoenix, Arizona, Association for Computing Machinery, 2016.
Version
Author's final manuscript
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 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 ε-optimal GPP (ε-GPP) policy. To plan in real time, we further propose an asymptotically optimal, branch-and-bound anytime variant of ε-GPP with performance guarantee. We empirically demonstrate the effectiveness of our ε-GPP policy and its anytime variant in Bayesian optimization and an energy harvesting task.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
http://dl.acm.org/citation.cfm?id=3016159
