\begin{thebibliography}{55}
\providecommand{\natexlab}[1]{#1}
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  \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi

\bibitem[Belakaria et~al.(2019)Belakaria, Deshwal, and Doppa]{belakaria2019max}
Syrine Belakaria, Aryan Deshwal, and Janardhan~Rao Doppa.
\newblock Max-value entropy search for multi-objective bayesian optimization.
\newblock In \emph{Advances in Neural Information Processing Systems},
  volume~32, 2019.

\bibitem[Belakaria et~al.(2020)Belakaria, Deshwal, and
  Doppa]{belakaria2020multi}
Syrine Belakaria, Aryan Deshwal, and Janardhan~Rao Doppa.
\newblock Multi-fidelity multi-objective bayesian optimization: An output space
  entropy search approach.
\newblock In \emph{Proceedings of the AAAI Conference on Artificial
  Intelligence}, volume~34, pages 10035--10043, 2020.

\bibitem[Belakaria et~al.(2023)Belakaria, Doppa, Fusi, and
  Sheth]{belakaria2023bayesian}
Syrine Belakaria, Janardhan~Rao Doppa, Nicolo Fusi, and Rishit Sheth.
\newblock Bayesian optimization over iterative learners with structured
  responses: A budget-aware planning approach.
\newblock In \emph{Proceedings of The 26th International Conference on
  Artificial Intelligence and Statistics}, pages 9076--9093, 2023.

\bibitem[Bergstra et~al.(2011)Bergstra, Bardenet, Bengio, and
  K{\'e}gl]{bergstra2011algorithms}
James Bergstra, R{\'e}mi Bardenet, Yoshua Bengio, and Bal{\'a}zs K{\'e}gl.
\newblock Algorithms for hyper-parameter optimization.
\newblock In \emph{Advances in Neural Information Processing Systems},
  volume~24, 2011.

\bibitem[Casimiro et~al.(2020)Casimiro, Didona, Romano, Rodrigues, Zwaenepoel,
  and Garlan]{casimiro2020lynceus}
Maria Casimiro, Diego Didona, Paolo Romano, Luis Rodrigues, Willy Zwaenepoel,
  and David Garlan.
\newblock Lynceus: Cost-efficient tuning and provisioning of data analytic
  jobs.
\newblock In \emph{2020 IEEE 40th International Conference on Distributed
  Computing Systems (ICDCS)}, pages 56--66, 2020.

\bibitem[Casimiro et~al.(2024)Casimiro, Soares, Garlan, Rodrigues, and
  Romano]{casimiro2024self}
Maria Casimiro, Diogo Soares, David Garlan, Lu{\'\i}s Rodrigues, and Paolo
  Romano.
\newblock Self-adapting machine learning-based systems via a probabilistic
  model checking framework.
\newblock \emph{ACM Transactions on Autonomous and Adaptive Systems}, 2024.

\bibitem[Dai et~al.(2019)Dai, Yu, Low, and Jaillet]{dai2019bayesian}
Zhongxiang Dai, Haibin Yu, Bryan Kian~Hsiang Low, and Patrick Jaillet.
\newblock Bayesian optimization meets bayesian optimal stopping.
\newblock In \emph{Proceedings of the 36th International Conference on Machine
  Learning}, volume~97, pages 1496--1506, 2019.

\bibitem[Daulton et~al.(2020)Daulton, Balandat, and
  Bakshy]{daulton2020differentiable}
Samuel Daulton, Maximilian Balandat, and Eytan Bakshy.
\newblock Differentiable expected hypervolume improvement for parallel
  multi-objective bayesian optimization.
\newblock In \emph{Advances in Neural Information Processing Systems},
  volume~33, pages 9851--9864, 2020.

\bibitem[Daulton et~al.(2021)Daulton, Balandat, and
  Bakshy]{daulton2021parallel}
Samuel Daulton, Maximilian Balandat, and Eytan Bakshy.
\newblock Parallel bayesian optimization of multiple noisy objectives with
  expected hypervolume improvement.
\newblock In \emph{Advances in Neural Information Processing Systems},
  volume~34, pages 2187--2200, 2021.

\bibitem[Daulton et~al.(2022)Daulton, Eriksson, Balandat, and
  Bakshy]{daulton2022multi}
Samuel Daulton, David Eriksson, Maximilian Balandat, and Eytan Bakshy.
\newblock Multi-objective bayesian optimization over high-dimensional search
  spaces.
\newblock In \emph{Proceedings of the 38th Uncertainty in Artificial
  Intelligence Conference}, pages 507--517, 2022.

\bibitem[Daxberger et~al.(2019)Daxberger, Makarova, Turchetta, and
  Krause]{daxberger2019mixed}
Erik Daxberger, Anastasia Makarova, Matteo Turchetta, and Andreas Krause.
\newblock Mixed-variable bayesian optimization.
\newblock \emph{arXiv preprint arXiv:1907.01329}, 2019.

\bibitem[Deb et~al.(2002)Deb, Thiele, Laumanns, and Zitzler]{deb2002scalable}
Kalyanmoy Deb, Lothar Thiele, Marco Laumanns, and Eckart Zitzler.
\newblock Scalable multi-objective optimization test problems.
\newblock In \emph{Proceedings of the 2002 Congress on Evolutionary
  Computation. CEC'02 (Cat. No. 02TH8600)}, volume~1, pages 825--830, 2002.

\bibitem[Eggensperger et~al.(2021)Eggensperger, M{\"u}ller, Mallik, Feurer,
  Sass, Klein, Awad, Lindauer, and Hutter]{eggensperger2021hpobench}
Katharina Eggensperger, Philipp M{\"u}ller, Neeratyoy Mallik, Matthias Feurer,
  Ren{\'e} Sass, Aaron Klein, Noor Awad, Marius Lindauer, and Frank Hutter.
\newblock Hpobench: A collection of reproducible multi-fidelity benchmark
  problems for hpo.
\newblock In \emph{Thirty-fifth Conference on Neural Information Processing
  Systems Datasets and Benchmarks Track (Round 2)}, 2021.

\bibitem[Emmerich et~al.(2006)Emmerich, Giannakoglou, and
  Naujoks]{emmerich2006single}
Michael~TM Emmerich, Kyriakos~C Giannakoglou, and Boris Naujoks.
\newblock Single-and multiobjective evolutionary optimization assisted by
  gaussian random field metamodels.
\newblock \emph{IEEE Transactions on Evolutionary Computation}, 10\penalty0
  (4):\penalty0 421--439, 2006.

\bibitem[Falkner et~al.(2018)Falkner, Klein, and Hutter]{falkner2018bohb}
Stefan Falkner, Aaron Klein, and Frank Hutter.
\newblock Bohb: Robust and efficient hyperparameter optimization at scale.
\newblock In \emph{Proceedings of the 35th International Conference on Machine
  Learning}, volume~80, pages 1437--1446, 2018.

\bibitem[Fan et~al.(2024)Fan, Yoon, Dougherty, Alexander, Urban, Arroyave, and
  Qian]{fan2024multi}
Mingzhou Fan, Byung-Jun Yoon, Edward Dougherty, Francis Alexander, Nathan
  Urban, Raymundo Arroyave, and Xiaoning Qian.
\newblock Multi-fidelity bayesian optimization with multiple information
  sources of input-dependent fidelity.
\newblock In \emph{Proceedings of the 40th Uncertainty in Artificial
  Intelligence Conference}, 2024.

\bibitem[Foldager et~al.(2023)Foldager, Jordahn, Hansen, and
  Andersen]{foldager2023role}
Jonathan Foldager, Mikkel Jordahn, Lars~K Hansen, and Michael~R Andersen.
\newblock On the role of model uncertainties in bayesian optimisation.
\newblock In \emph{Proceedings of the 39th Uncertainty in Artificial
  Intelligence Conference}, pages 592--601, 2023.

\bibitem[Gardner et~al.(2018)Gardner, Pleiss, Weinberger, Bindel, and
  Wilson]{gardner2018gpytorch}
Jacob Gardner, Geoff Pleiss, Kilian~Q Weinberger, David Bindel, and Andrew~G
  Wilson.
\newblock Gpytorch: Blackbox matrix-matrix gaussian process inference with gpu
  acceleration.
\newblock In \emph{Advances in Neural Information Processing Systems},
  volume~31, 2018.

\bibitem[Gijsbers et~al.(2019)Gijsbers, LeDell, Thomas, Poirier, Bischl, and
  Vanschoren]{gijsbers2019open}
Pieter Gijsbers, Erin LeDell, Janek Thomas, S{\'e}bastien Poirier, Bernd
  Bischl, and Joaquin Vanschoren.
\newblock An open source automl benchmark.
\newblock \emph{arXiv preprint arXiv:1907.00909}, 2019.

\bibitem[Hern{\'a}ndez-Lobato et~al.(2016)Hern{\'a}ndez-Lobato,
  Hernandez-Lobato, Shah, and Adams]{hernandez2016predictive}
Daniel Hern{\'a}ndez-Lobato, Jose Hernandez-Lobato, Amar Shah, and Ryan Adams.
\newblock Predictive entropy search for multi-objective bayesian optimization.
\newblock In \emph{Proceedings of the 33rd International Conference on Machine
  Learning}, volume~48, pages 1492--1501, 2016.

\bibitem[Hupkens et~al.(2015)Hupkens, Deutz, Yang, and
  Emmerich]{hupkens2015faster}
Iris Hupkens, Andr{\'e} Deutz, Kaifeng Yang, and Michael Emmerich.
\newblock Faster exact algorithms for computing expected hypervolume
  improvement.
\newblock In \emph{Proceedings of the International Conference on Evolutionary
  Multi-Criterion Optimization}, pages 65--79, 2015.

\bibitem[Jones et~al.(1998)Jones, Schonlau, and Welch]{jones1998efficient}
Donald~R Jones, Matthias Schonlau, and William~J Welch.
\newblock Efficient global optimization of expensive black-box functions.
\newblock \emph{Journal of Global optimization}, 13:\penalty0 455--492, 1998.

\bibitem[Kandasamy et~al.(2016)Kandasamy, Dasarathy, Oliva, Schneider, and
  P{\'o}czos]{kandasamy2016gaussian}
Kirthevasan Kandasamy, Gautam Dasarathy, Junier~B Oliva, Jeff Schneider, and
  Barnab{\'a}s P{\'o}czos.
\newblock Gaussian process bandit optimisation with multi-fidelity evaluations.
\newblock In \emph{Advances in Neural Information Processing Systems},
  volume~29, 2016.

\bibitem[Kandasamy et~al.(2017)Kandasamy, Dasarathy, Schneider, and
  P{\'o}czos]{kandasamy2017multi}
Kirthevasan Kandasamy, Gautam Dasarathy, Jeff Schneider, and Barnab{\'a}s
  P{\'o}czos.
\newblock Multi-fidelity bayesian optimisation with continuous approximations.
\newblock In \emph{Proceedings of the 34th International Conference on Machine
  Learning}, volume~70, pages 1799--1808, 2017.

\bibitem[Karl et~al.(2023)Karl, Pielok, Moosbauer, Pfisterer, Coors, Binder,
  Schneider, Thomas, Richter, Lang, et~al.]{karl2023multi}
Florian Karl, Tobias Pielok, Julia Moosbauer, Florian Pfisterer, Stefan Coors,
  Martin Binder, Lennart Schneider, Janek Thomas, Jakob Richter, Michel Lang,
  et~al.
\newblock Multi-objective hyperparameter optimization in machine learning —
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\newblock \emph{ACM Transactions on Evolutionary Learning and Optimization},
  3\penalty0 (4):\penalty0 1--50, 2023.

\bibitem[Klein et~al.(2017)Klein, Falkner, Bartels, Hennig, and
  Hutter]{klein2017fast}
Aaron Klein, Stefan Falkner, Simon Bartels, Philipp Hennig, and Frank Hutter.
\newblock Fast bayesian optimization of machine learning hyperparameters on
  large datasets.
\newblock In \emph{Proceedings of the 20th International Conference on
  Artificial Intelligence and Statistics}, volume~54, pages 528--536, 2017.

\bibitem[Klein et~al.(2022)Klein, Falkner, Springenberg, and
  Hutter]{klein2022learning}
Aaron Klein, Stefan Falkner, Jost~Tobias Springenberg, and Frank Hutter.
\newblock Learning curve prediction with bayesian neural networks.
\newblock In \emph{International Conference on Learning Representations}, 2022.

\bibitem[Knowles(2006)]{knowles2006parego}
Joshua Knowles.
\newblock Parego: A hybrid algorithm with on-line landscape approximation for
  expensive multiobjective optimization problems.
\newblock \emph{IEEE Transactions on Evolutionary Computation}, 10\penalty0
  (1):\penalty0 50--66, 2006.

\bibitem[L{\'e}vesque et~al.(2016)L{\'e}vesque, Gagn{\'e}, and
  Sabourin]{levesque2016bayesian}
Julien-Charles L{\'e}vesque, Christian Gagn{\'e}, and Robert Sabourin.
\newblock Bayesian hyperparameter optimization for ensemble learning.
\newblock In \emph{Proceedings of the 32nd Uncertainty in Artificial
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\bibitem[Li et~al.(2018)Li, Jamieson, DeSalvo, Rostamizadeh, and
  Talwalkar]{li2018hyperband}
Lisha Li, Kevin Jamieson, Giulia DeSalvo, Afshin Rostamizadeh, and Ameet
  Talwalkar.
\newblock Hyperband: A novel bandit-based approach to hyperparameter
  optimization.
\newblock \emph{Journal of Machine Learning Research}, 18\penalty0
  (185):\penalty0 1--52, 2018.

\bibitem[Mahadevan and Mathioudakis(2024)]{mahadevan2024cost}
Ananth Mahadevan and Michael Mathioudakis.
\newblock Cost-aware retraining for machine learning.
\newblock \emph{Knowledge-Based Systems}, 293:\penalty0 111610, 2024.

\bibitem[Martinez-Cantin(2018)]{martinez2018funneled}
Ruben Martinez-Cantin.
\newblock Funneled bayesian optimization for design, tuning and control of
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\newblock \emph{IEEE Transactions on Cybernetics}, 49\penalty0 (4):\penalty0
  1489--1500, 2018.

\bibitem[Mendes et~al.(2020)Mendes, Casimiro, Romano, and
  Garlan]{mendes2020trimtuner}
Pedro Mendes, Maria Casimiro, Paolo Romano, and David Garlan.
\newblock Trimtuner: Efficient optimization of machine learning jobs in the
  cloud via sub-sampling.
\newblock In \emph{28th International Symposium on Modeling, Analysis, and
  Simulation of Computer and Telecommunication Systems (MASCOTS)}, pages 1--8,
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\bibitem[Morales-Hern{\'a}ndez et~al.(2023)Morales-Hern{\'a}ndez,
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Alejandro Morales-Hern{\'a}ndez, Inneke Van~Nieuwenhuyse, and Sebastian
  Rojas~Gonzalez.
\newblock A survey on multi-objective hyperparameter optimization algorithms
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\newblock \emph{Artificial Intelligence Review}, 56\penalty0 (8):\penalty0
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\bibitem[Nguyen et~al.(2020)Nguyen, Schulze, and Osborne]{nguyen2020bayesian}
Vu~Nguyen, Sebastian Schulze, and Michael Osborne.
\newblock Bayesian optimization for iterative learning.
\newblock In \emph{Advances in Neural Information Processing Systems},
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\bibitem[Paria et~al.(2020)Paria, Kandasamy, and P{\'o}czos]{paria2020flexible}
Biswajit Paria, Kirthevasan Kandasamy, and Barnab{\'a}s P{\'o}czos.
\newblock A flexible framework for multi-objective bayesian optimization using
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\newblock In \emph{Proceedings of the 35th Uncertainty in Artificial
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\bibitem[Perrone et~al.(2018)Perrone, Jenatton, Seeger, and
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Valerio Perrone, Rodolphe Jenatton, Matthias~W Seeger, and C{\'e}dric
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\newblock Scalable hyperparameter transfer learning.
\newblock In \emph{Advances in Neural Information Processing Systems},
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\bibitem[Pfisterer et~al.(2022)Pfisterer, Schneider, Moosbauer, Binder, and
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Florian Pfisterer, Lennart Schneider, Julia Moosbauer, Martin Binder, and Bernd
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\newblock Yahpo gym-an efficient multi-objective multi-fidelity benchmark for
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\newblock In \emph{Proceedings of the First International Conference on
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Carl~Edward Rasmussen and Christopher K.~I. Williams.
\newblock \emph{Gaussian processes for machine learning}.
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\bibitem[Regis and Shoemaker(2007)]{regis2007stochastic}
Rommel~G Regis and Christine~A Shoemaker.
\newblock A stochastic radial basis function method for the global optimization
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\newblock \emph{INFORMS Journal on Computing}, 19\penalty0 (4):\penalty0
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Mark Sandler, Andrew Howard, Menglong Zhu, Andrey Zhmoginov, and Liang-Chieh
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\newblock Mobilenetv2: Inverted residuals and linear bottlenecks.
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Robin Schmucker, Michele Donini, Muhammad~Bilal Zafar, David Salinas, and
  C{\'e}dric Archambeau.
\newblock Multi-objective asynchronous successive halving.
\newblock \emph{arXiv preprint arXiv:2106.12639}, 2021.

\bibitem[Sen et~al.(2018)Sen, Kandasamy, and Shakkottai]{sen2018multi}
Rajat Sen, Kirthevasan Kandasamy, and Sanjay Shakkottai.
\newblock Multi-fidelity black-box optimization with hierarchical partitions.
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Niranjan Srinivas, Andreas Krause, Sham~M Kakade, and Matthias Seeger.
\newblock Gaussian process optimization in the bandit setting: No regret and
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Shinya Suzuki, Shion Takeno, Tomoyuki Tamura, Kazuki Shitara, and Masayuki
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\newblock Multi-objective bayesian optimization using pareto-frontier entropy.
\newblock In \emph{Proceedings of the 37th International Conference on Machine
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Kevin Swersky, Jasper Snoek, and Ryan~Prescott Adams.
\newblock Freeze-thaw bayesian optimization.
\newblock \emph{arXiv preprint arXiv:1406.3896}, 2014.

\bibitem[Thompson(1933)]{thompson1933likelihood}
William~R Thompson.
\newblock On the likelihood that one unknown probability exceeds another in
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\newblock Openml: networked science in machine learning.
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\bibitem[Wang and Shoemaker(2023)]{wang2023reference}
Wenyu Wang and Christine~A Shoemaker.
\newblock Reference vector assisted candidate search with aggregated surrogate
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\newblock \emph{INFORMS Journal on Computing}, 35\penalty0 (2):\penalty0
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Wenyu Wang, Taimoor Akhtar, and Christine~A Shoemaker.
\newblock Efficient multi-objective optimization through parallel
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Jian Wu, Saul Toscano-Palmerin, Peter~I Frazier, and Andrew~Gordon Wilson.
\newblock Practical multi-fidelity bayesian optimization for hyperparameter
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Kaifeng Yang, Michael Affenzeller, and Guozhi Dong.
\newblock A parallel technique for multi-objective bayesian global
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\newblock \emph{Swarm and Evolutionary Computation}, 75:\penalty0 101183, 2022.

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\newblock Auto-pytorch: Multi-fidelity metalearning for efficient and robust
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\bibitem[Zitzler et~al.(2000)Zitzler, Deb, and Thiele]{zitzler2000comparison}
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\end{thebibliography}
