@article{wang2016bayesian,
  title={Bayesian optimization in a billion dimensions via random embeddings},
  author={Wang, Ziyu and Hutter, Frank and Zoghi, Masrour and Matheson, David and De Feitas, Nando},
  journal={Journal of Artificial Intelligence Research},
  volume={55},
  pages={361--387},
  year={2016}
}

@article{letham2020re,
  title={Re-examining linear embeddings for high-dimensional Bayesian optimization},
  author={Letham, Ben and Calandra, Roberto and Rai, Akshara and Bakshy, Eytan},
  journal={Advances in neural information processing systems},
  volume={33},
  pages={1546--1558},
  year={2020}
}

@article{yi2024improving,
  title={Improving sample efficiency of high dimensional Bayesian optimization with MCMC},
  author={Yi, Zeji and Wei, Yunyue and Cheng, Chu Xin and He, Kaibo and Sui, Yanan},
  journal={arXiv preprint arXiv:2401.02650},
  year={2024}
}

@inproceedings{eriksson2021high,
  title={High-dimensional Bayesian optimization with sparse axis-aligned subspaces},
  author={Eriksson, David and Jankowiak, Martin},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={493--503},
  year={2021},
  organization={PMLR}
}

@inproceedings{dasgupta1999learning,
  title={Learning mixtures of Gaussians},
  author={Dasgupta, Sanjoy},
  booktitle={40th Annual Symposium on Foundations of Computer Science (Cat. No. 99CB37039)},
  pages={634--644},
  year={1999},
  organization={IEEE}
}

@inproceedings{nayebi2019framework,
  title={A framework for Bayesian optimization in embedded subspaces},
  author={Nayebi, Amin and Munteanu, Alexander and Poloczek, Matthias},
  booktitle={International Conference on Machine Learning},
  pages={4752--4761},
  year={2019},
  organization={PMLR}
}

@article{hellsten2023high,
  title={High-dimensional Bayesian Optimization with Group Testing},
  author={Hellsten, Erik Orm and Hvarfner, Carl and Papenmeier, Leonard and Nardi, Luigi},
  journal={arXiv preprint arXiv:2310.03515},
  year={2023}
}

@article{binois2022survey,
  title={A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization},
  author={Binois, Mickael and Wycoff, Nathan},
  journal={ACM Transactions on Evolutionary Learning and Optimization},
  volume={2},
  number={2},
  pages={1--26},
  year={2022},
  publisher={ACM New York, NY}
}

@article{hvarfner2024self,
  title={Self-correcting bayesian optimization through bayesian active learning},
  author={Hvarfner, Carl and Hellsten, Erik and Hutter, Frank and Nardi, Luigi},
  journal={Advances in Neural Information Processing Systems},
  volume={36},
  year={2024}
}

@article{berkenkamp2019no,
  title={No-regret bayesian optimization with unknown hyperparameters},
  author={Berkenkamp, Felix and Schoellig, Angela P and Krause, Andreas},
  journal={Journal of Machine Learning Research},
  volume={20},
  number={50},
  pages={1--24},
  year={2019}
}

@article{wang2024constrained,
  title={Constrained Bayesian optimization with merit functions},
  author={Wang, Jingyi and Petra, Cosmin G and Peterson, J Luc},
  journal={arXiv preprint arXiv:2403.13140},
  year={2024}
}

@article{antonio2021sequential,
  title={Sequential model based optimization of partially defined functions under unknown constraints},
  author={Antonio, Candelieri},
  journal={Journal of Global Optimization},
  volume={79},
  number={2},
  pages={281--303},
  year={2021},
  publisher={Springer}
}

@article{donskoi1993partially,
  title={Partially defined optimization problems: An approach to a solution that is based on pattern recognition theory},
  author={Donskoi, VI},
  journal={Journal of Soviet Mathematics},
  volume={65},
  pages={1664--1668},
  year={1993},
  publisher={Springer}
}

@article{rudenko1994objective,
  title={Objective functional approximation in a partially defined optimization problem},
  author={Rudenko, LI},
  journal={Journal of Mathematical Sciences},
  volume={72},
  pages={3359--3363},
  year={1994},
  publisher={Springer}
}

@article{sergeyev2007one,
  title={A one-dimensional local tuning algorithm for solving GO problems with partially defined constraints},
  author={Sergeyev, Yaroslav D and Kvasov, Dmitri E and Khalaf, Falah MH},
  journal={Optimization Letters},
  volume={1},
  number={1},
  pages={85--99},
  year={2007},
  publisher={Springer}
}

@inproceedings{chowdhury2017kernelized,
  title={On kernelized multi-armed bandits},
  author={Chowdhury, Sayak Ray and Gopalan, Aditya},
  booktitle={International Conference on Machine Learning},
  pages={844--853},
  year={2017},
  organization={PMLR}
}

@article{gelbart2014bayesian,
  title={Bayesian optimization with unknown constraints},
  author={Gelbart, Michael A and Snoek, Jasper and Adams, Ryan P},
  journal={arXiv preprint arXiv:1403.5607},
  year={2014}
}

@inproceedings{gotovos2013active,
  title={Active learning for level set estimation},
  author={Gotovos, Alkis and Casati, Nathalie and Hitz, Gregory and Krause, Andreas},
  booktitle={Proceedings of the Twenty-Third international joint conference on Artificial Intelligence},
  pages={1344--1350},
  year={2013}
}
@book{williams2006gaussian,
  title={Gaussian processes for machine learning},
  author={Williams, Christopher KI and Rasmussen, Carl Edward},
  volume={2},
  year={2006},
  publisher={MIT press Cambridge, MA}
}
@inproceedings{sui2015safe,
  title={Safe exploration for optimization with Gaussian processes},
  author={Sui, Yanan and Gotovos, Alkis and Burdick, Joel and Krause, Andreas},
  booktitle={International conference on machine learning},
  pages={997--1005},
  year={2015},
  organization={PMLR}
}
@article{gramacy2016modeling,
  title={Modeling an augmented Lagrangian for blackbox constrained optimization},
  author={Gramacy, Robert B and Gray, Genetha A and Le Digabel, S{\'e}bastien and Lee, Herbert KH and Ranjan, Pritam and Wells, Garth and Wild, Stefan M},
  journal={Technometrics},
  volume={58},
  number={1},
  pages={1--11},
  year={2016},
  publisher={Taylor \& Francis}
}
@article{bogunovic2016truncated,
  title={Truncated variance reduction: A unified approach to bayesian optimization and level-set estimation},
  author={Bogunovic, Ilija and Scarlett, Jonathan and Krause, Andreas and Cevher, Volkan},
  journal={Advances in neural information processing systems},
  volume={29},
  year={2016}
}
@inproceedings{nguyen2021information,
  title={An information-theoretic framework for unifying active learning problems},
  author={Nguyen, Quoc Phong and Low, Bryan Kian Hsiang and Jaillet, Patrick},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  pages={9126--9134},
  year={2021}
}
@article{frazier2018tutorial,
  title={A tutorial on Bayesian optimization},
  author={Frazier, Peter I},
  journal={arXiv preprint arXiv:1807.02811},
  year={2018}
}
@article{schonlau1998global,
  title={Global versus local search in constrained optimization of computer models},
  author={Schonlau, Matthias and Welch, William J and Jones, Donald R},
  journal={Lecture notes-monograph series},
  pages={11--25},
  year={1998},
  publisher={JSTOR}
}
@inproceedings{gardner2014bayesian,
  title={Bayesian optimization with inequality constraints.},
  author={Gardner, Jacob R and Kusner, Matt J and Xu, Zhixiang Eddie and Weinberger, Kilian Q and Cunningham, John P},
  booktitle={ICML},
  volume={2014},
  pages={937--945},
  year={2014}
}
@article{letham2019constrained,
  title={Constrained Bayesian optimization with noisy experiments},
  author={Letham, Benjamin and Karrer, Brian and Ottoni, Guilherme and Bakshy, Eytan},
  journal={Bayesian Analysis},
  volume={14},
  number={2},
  pages={495--519},
  year={2019},
  publisher={International Society for Bayesian Analysis}
}
@article{picheny2016bayesian,
  title={Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian},
  author={Picheny, Victor and Gramacy, Robert B and Wild, Stefan and Le Digabel, Sebastien},
  journal={Advances in neural information processing systems},
  volume={29},
  year={2016}
}
@article{ariafar2019admmbo,
  title={ADMMBO: Bayesian Optimization with Unknown Constraints using ADMM.},
  author={Ariafar, Setareh and Coll-Font, Jaume and Brooks, Dana H and Dy, Jennifer G},
  journal={J. Mach. Learn. Res.},
  volume={20},
  number={123},
  pages={1--26},
  year={2019}
}
@inproceedings{hernandez2015predictive,
  title={Predictive entropy search for Bayesian optimization with unknown constraints},
  author={Hern{\'a}ndez-Lobato, Jos{\'e} Miguel and Gelbart, Michael and Hoffman, Matthew and Adams, Ryan and Ghahramani, Zoubin},
  booktitle={International conference on machine learning},
  pages={1699--1707},
  year={2015},
  organization={PMLR}
}
@article{hernandez2014predictive,
  title={Predictive entropy search for efficient global optimization of black-box functions},
  author={Hern{\'a}ndez-Lobato, Jos{\'e} Miguel and Hoffman, Matthew W and Ghahramani, Zoubin},
  journal={Advances in neural information processing systems},
  volume={27},
  year={2014}
}
@inproceedings{wang2017max,
  title={Max-value entropy search for efficient Bayesian optimization},
  author={Wang, Zi and Jegelka, Stefanie},
  booktitle={International Conference on Machine Learning},
  pages={3627--3635},
  year={2017},
  organization={PMLR}
}
@article{perrone2019constrained,
  title={Constrained bayesian optimization with max-value entropy search},
  author={Perrone, Valerio and Shcherbatyi, Iaroslav and Jenatton, Rodolphe and Archambeau, Cedric and Seeger, Matthias},
  journal={arXiv preprint arXiv:1910.07003},
  year={2019}
}
@inproceedings{takeno2022sequential,
  title={Sequential and Parallel Constrained Max-value Entropy Search via Information Lower Bound},
  author={Takeno, Shion and Tamura, Tomoyuki and Shitara, Kazuki and Karasuyama, Masayuki},
  booktitle={International Conference on Machine Learning},
  pages={20960--20986},
  year={2022},
  organization={PMLR}
}


@inproceedings{eriksson2021scalable,
  title={Scalable constrained Bayesian optimization},
  author={Eriksson, David and Poloczek, Matthias},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={730--738},
  year={2021},
  organization={PMLR}
}

@article{wilson2010copula,
  title={Copula processes},
  author={Wilson, Andrew G and Ghahramani, Zoubin},
  journal={Advances in Neural Information Processing Systems},
  volume={23},
  year={2010}
}

@article{eriksson2019scalable,
  title={Scalable global optimization via local bayesian optimization},
  author={Eriksson, David and Pearce, Michael and Gardner, Jacob and Turner, Ryan D and Poloczek, Matthias},
  journal={Advances in neural information processing systems},
  volume={32},
  year={2019}
}

@article{makarova2021risk,
  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}
}

@book{rasmussen:williams:2006,
  added-at = {2009-03-05T08:49:50.000+0100},
  author = {Rasmussen, C. E. and Williams, C. K. I.},
  biburl = {https://www.bibsonomy.org/bibtex/26771eaebbee7d852934f29aa33dea971/bcao},
  interhash = {72c030472023000e0bdeeb06081c3764},
  intrahash = {6771eaebbee7d852934f29aa33dea971},
  keywords = {},
  publisher = {MIT Press},
  timestamp = {2009-03-05T08:49:50.000+0100},
  title = {Gaussian Processes for Machine Learning},
  year = 2006,
  @URL={https://bit.ly/2tYpBix}
}

@article{koepernik2021consistency,
  title={Consistency of Gaussian process regression in metric spaces},
  author={Koepernik, Peter and Pfaff, Florian},
  journal={The Journal of Machine Learning Research},
  volume={22},
  number={1},
  pages={11066--11092},
  year={2021},
  publisher={JMLRORG}
}

@article{even2006action,
  title={Action Elimination and Stopping Conditions for the Multi-Armed Bandit and Reinforcement Learning Problems.},
  author={Even-Dar, Eyal and Mannor, Shie and Mansour, Yishay and Mahadevan, Sridhar},
  journal={Journal of machine learning research},
  volume={7},
  number={6},
  year={2006}
}

@article{srinivas2009gaussian,
  title={Gaussian process optimization in the bandit setting: No regret and experimental design},
  author={Srinivas, Niranjan and Krause, Andreas and Kakade, Sham M and Seeger, Matthias},
  journal={arXiv preprint arXiv:0912.3995},
  year={2009}
}

@inproceedings{malkomes2021beyond,
  title={Beyond the pareto efficient frontier: Constraint active search for multiobjective experimental design},
  author={Malkomes, Gustavo and Cheng, Bolong and Lee, Eric H and Mccourt, Mike},
  booktitle={International Conference on Machine Learning},
  pages={7423--7434},
  year={2021},
  organization={PMLR}
}

@article{tanabe2020easy,
  title={An easy-to-use real-world multi-objective optimization problem suite},
  author={Tanabe, Ryoji and Ishibuchi, Hisao},
  journal={Applied Soft Computing},
  volume={89},
  pages={106078},
  year={2020},
  publisher={Elsevier}
}

@misc{misc_wave_energy_converters_534,
  title={{Wave Energy Converters}},
  year={2019},
  howpublished={UCI Machine Learning Repository},
  note={{DOI}: https://doi.org/10.24432/C5QS4V},
}

@article{10018403158,
  title={Systems of extremal control},
  author={Rastrigin, Leonard Andreevi{\v{c}}},
  journal={Nauka},
  year={1974}
}

@article{pohlheimgeatbx,
  title={Geatbx examples examples of objective functions},
  year={2006},
  author={Pohlheim, H},
  journal={URL http://www. geatbx. com/download/GEATbx\_ObjFunExpl\_v37. pdf}
}

@article{balandat2020botorch,
  title={BoTorch: A framework for efficient Monte-Carlo Bayesian optimization},
  author={Balandat, Maximilian and Karrer, Brian and Jiang, Daniel and Daulton, Samuel and Letham, Ben and Wilson, Andrew G and Bakshy, Eytan},
  journal={Advances in neural information processing systems},
  volume={33},
  pages={21524--21538},
  year={2020}
}

@article{deb2013evolutionary,
  title={An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints},
  author={Deb, Kalyanmoy and Jain, Himanshu},
  journal={IEEE transactions on evolutionary computation},
  volume={18},
  number={4},
  pages={577--601},
  year={2013},
  publisher={IEEE}
}

@inproceedings{lampinen1999mixed,
  title={Mixed integer-discrete-continuous optimization by differential evolution},
  author={Lampinen, Jouni and Zelinka, Ivan},
  booktitle={Proceedings of the 5th international conference on soft computing},
  pages={71--76},
  year={1999},
  organization={Citeseer}
}

@article{kannan1994augmented,
  title={An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design},
  author={Kannan, BK and Kramer, SN},
  journal={Journal of Mechanical Design},
  volume={116},
  number={2},
  pages={405--411},
  year={1994},
  publisher={ASME International}
}

@misc{zhang2023learning,
      title={Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set Estimation}, 
      author={Fengxue Zhang and Jialin Song and James Bowden and Alexander Ladd and Yisong Yue and Thomas A. Desautels and Yuxin Chen},
      year={2023},
      eprint={2307.13371},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

@article{komiyama2022bridging,
  title={Bridging Offline and Online Experimentation: Constraint Active Search for Deployed Performance Optimization},
  author={Komiyama, Junpei and Malkomes, Gustavo and Cheng, Bolong and McCourt, Michael},
  journal={Transactions on Machine Learning Research},
  year={2022}
}

@article{lu2022no,
  title={No-regret Bayesian optimization with unknown equality and inequality constraints using exact penalty functions},
  author={Lu, Congwen and Paulson, Joel A},
  journal={IFAC-PapersOnLine},
  volume={55},
  number={7},
  pages={895--902},
  year={2022},
  publisher={Elsevier}
}

@inproceedings{xu2023constrained,
  title={Constrained efficient global optimization of expensive black-box functions},
  author={Xu, Wenjie and Jiang, Yuning and Svetozarevic, Bratislav and Jones, Colin},
  booktitle={International Conference on Machine Learning},
  pages={38485--38498},
  year={2023},
  organization={PMLR}
}

@article{zhou2022kernelized,
  title={On kernelized multi-armed bandits with constraints},
  author={Zhou, Xingyu and Ji, Bo},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={14--26},
  year={2022}
}

@article{paulson2022cobalt,
  title={COBALT: COnstrained Bayesian optimizAtion of computationaLly expensive grey-box models exploiting derivaTive information},
  author={Paulson, Joel A and Lu, Congwen},
  journal={Computers \& Chemical Engineering},
  volume={160},
  pages={107700},
  year={2022},
  publisher={Elsevier}
}

@article{mackay1992information,
  title={Information-based objective functions for active data selection},
  author={MacKay, David JC},
  journal={Neural computation},
  volume={4},
  number={4},
  pages={590--604},
  year={1992},
  publisher={MIT Press One Rogers Street, Cambridge, MA 02142-1209, USA journals-info~…}
}


@article{lu2023no,
  title={No-regret constrained Bayesian optimization of noisy and expensive hybrid models using differentiable quantile function approximations},
  author={Lu, Congwen and Paulson, Joel A},
  journal={arXiv preprint arXiv:2305.03824},
  year={2023}
}

@article{feliot2017bayesian,
  title={A Bayesian approach to constrained single-and multi-objective optimization},
  author={Feliot, Paul and Bect, Julien and Vazquez, Emmanuel},
  journal={Journal of Global Optimization},
  volume={67},
  number={1-2},
  pages={97--133},
  year={2017},
  publisher={Springer}
}


@InProceedings{pmlr-v211-guo23a,
  title = 	 {Rectified Pessimistic-Optimistic Learning for Stochastic Continuum-armed Bandit with Constraints},
  author =       {Guo, Hengquan and Qi, Zhu and Liu, Xin},
  booktitle = 	 {Proceedings of The 5th Annual Learning for Dynamics and Control Conference},
  pages = 	 {1333--1344},
  year = 	 {2023},
  editor = 	 {Matni, Nikolai and Morari, Manfred and Pappas, George J.},
  volume = 	 {211},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {15--16 Jun},
  publisher =    {PMLR},
  pdf = 	 {https://proceedings.mlr.press/v211/guo23a/guo23a.pdf},
  url = 	 {https://proceedings.mlr.press/v211/guo23a.html},
  abstract = 	 {This paper studies the problem of stochastic continuum-armed bandit with constraints (SCBwC), where we optimize a black-box reward function $f(x)$ subject to a black-box constraint function $g(x)\leq 0$ over a continuous space $\mathcal X$. We model reward and constraint functions via Gaussian processes (GPs) and propose a Rectified Pessimistic-Optimistic Learning (RPOL) framework, a penalty-based method incorporating optimistic and pessimistic GP bandit learning for reward and constraint functions, respectively.  We consider the metric of cumulative constraint violation $\sum_{t=1}^T(g(x_t))^{+},$ which is strictly stronger than the traditional long-term constraint violation $\sum_{t=1}^Tg(x_t).$  The rectified design for the penalty update and the pessimistic learning for the constraint function in RPOL guarantee the cumulative constraint violation is minimal. RPOL can achieve sublinear regret and cumulative constraint violation for SCBwC and its variants (e.g., under delayed feedback). These theoretical results match their unconstrained counterparts. Our experiments justify RPOL outperforms several existing baseline algorithms.}
}


@article{camilleri2022active,
  title={Active Learning with Safety Constraints},
  author={Camilleri, Romain and Wagenmaker, Andrew and Morgenstern, Jamie H and Jain, Lalit and Jamieson, Kevin G},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={33201--33214},
  year={2022}
}

@book{garnett_bayesoptbook_2023,
  author    = {Garnett, Roman},
  title     = {{Bayesian Optimization}},
  year      = {2023},
  publisher = {Cambridge University Press}
}

@book{gramacy2020surrogates,
  title={Surrogates: Gaussian process modeling, design, and optimization for the applied sciences},
  author={Gramacy, Robert B},
  year={2020},
  publisher={Chapman and Hall/CRC}
}

@misc{digabel2015taxonomyconstraintssimulationbasedoptimization,
      title={A Taxonomy of Constraints in Simulation-Based Optimization}, 
      author={Sébastien Le Digabel and Stefan M. Wild},
      year={2015},
      eprint={1505.07881},
      archivePrefix={arXiv},
      primaryClass={math.OC},
      url={https://arxiv.org/abs/1505.07881}, 
}

@article{bernardo2011optimization,
  title={Optimization under unknown constraints},
  author={Bernardo, J and Bayarri, MJ and Berger, JO and Dawid, AP and Heckerman, D and Smith, AFM and West, M},
  journal={Bayesian Statistics},
  volume={9},
  number={9},
  pages={229},
  year={2011}
}

@article{zhang2021constrained,
  title={Constrained two-step look-ahead Bayesian optimization},
  author={Zhang, Yunxiang and Zhang, Xiangyu and Frazier, Peter},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={12563--12575},
  year={2021}
}

@article{sacher2018classification,
  title={A classification approach to efficient global optimization in presence of non-computable domains},
  author={Sacher, Matthieu and Duvigneau, R{\'e}gis and Le Maitre, Olivier and Durand, Mathieu and Berrini, Elisa and Hauville, Fr{\'e}d{\'e}ric and Astolfi, Jacques-Andr{\'e}},
  journal={Structural and Multidisciplinary Optimization},
  volume={58},
  pages={1537--1557},
  year={2018},
  publisher={Springer}
}

@article{bachoc2020gaussian,
  title={Gaussian process optimization with failures: classification and convergence proof},
  author={Bachoc, Fran{\c{c}}ois and Helbert, C{\'e}line and Picheny, Victor},
  journal={Journal of Global Optimization},
  volume={78},
  number={3},
  pages={483--506},
  year={2020},
  publisher={Springer}
}

@article{bect2012sequential,
  title={Sequential design of computer experiments for the estimation of a probability of failure},
  author={Bect, Julien and Ginsbourger, David and Li, Ling and Picheny, Victor and Vazquez, Emmanuel},
  journal={Statistics and Computing},
  volume={22},
  pages={773--793},
  year={2012},
  publisher={Springer}
}

@inproceedings{wilson2016deep,
  title={Deep kernel learning},
  author={Wilson, Andrew Gordon and Hu, Zhiting and Salakhutdinov, Ruslan and Xing, Eric P},
  booktitle={Artificial intelligence and statistics},
  pages={370--378},
  year={2016},
  organization={PMLR}
}

