%0 Conference Paper %1 pmlr-v89-song19b %A Song, Jialin %A Chen, Yuxin %A Yue, Yisong %B Proceedings of Machine Learning Research %D 2019 %E Chaudhuri, Kamalika %E Sugiyama, Masashi %I PMLR %K bayesian gaussian-proceses %P 3158--3167 %T A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes %U http://proceedings.mlr.press/v89/song19b.html %V 89 %X 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 physical system, intelligently trading off computer simulations and real-world tests can lead to significant savings. Existing multi-fidelity Bayesian optimization 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 relationships with the target function. Then we use cost-sensitive mutual information gain for efficient Bayesian optimization. We propose a simple notion of regret which incorporates the varying 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.

@inproceedings{pmlr-v89-song19b, 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 physical system, intelligently trading off computer simulations and real-world tests can lead to significant savings. Existing multi-fidelity Bayesian optimization 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 relationships with the target function. Then we use cost-sensitive mutual information gain for efficient Bayesian optimization. We propose a simple notion of regret which incorporates the varying 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.}, added-at = {2019-12-11T13:50:01.000+0100}, author = {Song, Jialin and Chen, Yuxin and Yue, Yisong}, biburl = {https://www.bibsonomy.org/bibtex/2cbbee2dcba4e9c0ddeeedf516e32a96b/kirk86}, booktitle = {Proceedings of Machine Learning Research}, description = {A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, interhash = {f06e48cbb432ebec20844588559859d9}, intrahash = {cbbee2dcba4e9c0ddeeedf516e32a96b}, keywords = {bayesian gaussian-proceses}, month = {16--18 Apr}, pages = {3158--3167}, pdf = {http://proceedings.mlr.press/v89/song19b/song19b.pdf}, publisher = {PMLR}, series = {Proceedings of Machine Learning Research}, timestamp = {2019-12-11T13:50:01.000+0100}, title = {A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processes}, url = {http://proceedings.mlr.press/v89/song19b.html}, volume = 89, year = 2019 }