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A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes

Song, Jialin and Chen, Yuxin and Yue, Yisong (2018) A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20190205-101951355

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Abstract

How can we efficiently gather information to optimize an unknown function, when presented with multiple, mutually dependent information sources with different costs? For example, when optimizing a robotic system, intelligently trading off computer simulations and real robot testings can lead to significant savings. Existing methods, such as multi-fidelity GP-UCB or Entropy Search-based approaches, either make simplistic assumptions on the interaction among different fidelities or use simple heuristics that lack theoretical guarantees. In this paper, we study multi-fidelity Bayesian optimization with complex structural dependencies among multiple outputs, and propose MF-MI-Greedy, a principled algorithmic framework for addressing this problem. In particular, we model different fidelities using additive Gaussian processes based on shared latent structures with the target function. Then we use cost-sensitive mutual information gain for efficient Bayesian global optimization. We propose a simple notion of regret which incorporates the cost of different fidelities, and prove that MF-MI-Greedy achieves low regret. We demonstrate the strong empirical performance of our algorithm on both synthetic and real-world datasets.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1811.00755arXivDiscussion Paper
Additional Information:This work was supported in part by NSF Award #1645832, Northrop Grumman, Bloomberg, and a Swiss NSF Early Mobility Postdoctoral Fellowship.
Funders:
Funding AgencyGrant Number
NSFCNS-1645832
Northrop GrummanUNSPECIFIED
Bloomberg Data ScienceUNSPECIFIED
Swiss National Science Foundation (SNSF)UNSPECIFIED
Record Number:CaltechAUTHORS:20190205-101951355
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190205-101951355
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92661
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Feb 2019 19:03
Last Modified:05 Feb 2019 19:03

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