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  booktitle={International Conference on Machine Learning},
  pages={9334--9345},
  year={2020},
  organization={PMLR}
}

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@inproceedings{NIPS2016_605ff764,
 author = {Kandasamy, Kirthevasan and Dasarathy, Gautam and Oliva, Junier B and Schneider, Jeff and Poczos, Barnabas},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {D. Lee and M. Sugiyama and U. Luxburg and I. Guyon and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Gaussian Process Bandit Optimisation with Multi-fidelity Evaluations},
 url = {https://proceedings.neurips.cc/paper/2016/file/605ff764c617d3cd28dbbdd72be8f9a2-Paper.pdf},
 volume = {29},
 year = {2016}
}

@INPROCEEDINGS{7900023,
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  title={Hyperparameter tuning for big data using {Bayesian} optimisation}, 
  year={2016},
  volume={},
  number={},
  pages={2574-2579},
  doi={10.1109/ICPR.2016.7900023}}
  
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  year={2017},
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}

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}


@InProceedings{pmlr-v119-takeno20a,
  title = 	 {Multi-fidelity {B}ayesian Optimization with Max-value Entropy Search and its Parallelization},
  author =       {Takeno, Shion and Fukuoka, Hitoshi and Tsukada, Yuhki and Koyama, Toshiyuki and Shiga, Motoki and Takeuchi, Ichiro and Karasuyama, Masayuki},
  booktitle = 	 {Proceedings of the 37th International Conference on Machine Learning},
  pages = 	 {9334--9345},
  year = 	 {2020},
  editor = 	 {III, Hal Daumé and Singh, Aarti},
  volume = 	 {119},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {13--18 Jul},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v119/takeno20a/takeno20a.pdf},
  url = 	 {https://proceedings.mlr.press/v119/takeno20a.html},
  abstract = 	 {In a standard setting of Bayesian optimization (BO), the objective function evaluation is assumed to be highly expensive. Multi-fidelity Bayesian optimization (MFBO) accelerates BO by incorporating lower fidelity observations available with a lower sampling cost. We propose a novel information-theoretic approach to MFBO, called multi-fidelity max-value entropy search (MF-MES), that enables us to obtain a more reliable evaluation of the information gain compared with existing information-based methods for MFBO. Further, we also propose a parallelization of MF-MES mainly for the asynchronous setting because queries typically occur asynchronously in MFBO due to a variety of sampling costs. We show that most of computations in our acquisition functions can be derived analytically, except for at most only two dimensional numerical integration that can be performed efficiently by simple approximations. We demonstrate effectiveness of our approach by using benchmark datasets and a real-world application to materials science data.}
}
@inproceedings{zhang2017information,
  title={Information-based multi-fidelity {Bayesian} optimization},
  author={Zhang, Yehong and Hoang, Trong Nghia and Low, Bryan Kian Hsiang and Kankanhalli, Mohan},
  booktitle={NIPS Workshop on Bayesian Optimization},
  year={2017}
}
@inproceedings{NEURIPS2021_d5e2c0ad,
 author = {Li, Shibo and Kirby, Robert and Zhe, Shandian},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan},
 pages = {25463--25475},
 publisher = {Curran Associates, Inc.},
 title = {Batch Multi-Fidelity {Bayesian} Optimization with  Deep Auto-Regressive Networks},
 url = {https://proceedings.neurips.cc/paper/2021/file/d5e2c0adad503c91f91df240d0cd4e49-Paper.pdf},
 volume = {34},
 year = {2021}
}

@article{li2020multi,
  title={Multi-fidelity {Bayesian} optimization via deep neural networks},
  author={Li, Shibo and Xing, Wei and Kirby, Robert and Zhe, Shandian},
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  volume={33},
  pages={8521--8531},
  year={2020}
}

@inproceedings{lam2015multifidelity,
  title={Multifidelity optimization using statistical surrogate modeling for non-hierarchical information sources},
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  year={2015}
}

@inproceedings{song2019general,
  title={A general framework for multi-fidelity {Bayesian} optimization with {Gaussian processes}},
  author={Song, Jialin and Chen, Yuxin and Yue, Yisong},
  booktitle={The 22nd International Conference on Artificial Intelligence and Statistics},
  pages={3158--3167},
  year={2019},
  organization={PMLR}
}


@InProceedings{pmlr-v70-kandasamy17a,
  title = 	 {Multi-fidelity {B}ayesian Optimisation with Continuous Approximations},
  author =       {Kirthevasan Kandasamy and Gautam Dasarathy and Jeff Schneider and Barnab{\'a}s P{\'o}czos},
  booktitle = 	 {Proceedings of the 34th International Conference on Machine Learning},
  pages = 	 {1799--1808},
  year = 	 {2017},
  editor = 	 {Precup, Doina and Teh, Yee Whye},
  volume = 	 {70},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {06--11 Aug},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v70/kandasamy17a/kandasamy17a.pdf},
  url = 	 {https://proceedings.mlr.press/v70/kandasamy17a.html},
  abstract = 	 {Bandit methods for black-box optimisation, such as Bayesian optimisation, are used in a variety of applications including hyper-parameter tuning and experiment design. Recently, <em>multi-fidelity</em> methods have garnered considerable attention since function evaluations have become increasingly expensive in such applications. Multi-fidelity methods use cheap approximations to the function of interest to speed up the overall optimisation process. However, most multi-fidelity methods assume only a finite number of approximations. On the other hand, in many practical applications, a continuous spectrum of approximations might be available. For instance, when tuning an expensive neural network, one might choose to approximate the cross validation performance using less data $N$ and/or few training iterations $T$. Here, the approximations are best viewed as arising out of a continuous two dimensional space $(N,T)$. In this work, we develop a Bayesian optimisation method, BOCA, for this setting. We characterise its theoretical properties and show that it achieves better regret than than strategies which ignore the approximations. BOCA outperforms several other baselines in synthetic and real experiments.}
}

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@article{poloczek2017multi,
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@article{griffiths2021achieving,
  title={Achieving robustness to aleatoric uncertainty with heteroscedastic Bayesian optimisation},
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  title={Risk-averse heteroscedastic bayesian optimization},
  author={Makarova, Anastasia and Usmanova, Ilnura and Bogunovic, Ilija and Krause, Andreas},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={17235--17245},
  year={2021}
}

@article{tautvaivsas2023heteroscedastic,
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  journal={Journal of Global Optimization},
  pages={1--21},
  year={2023},
  publisher={Springer}
}