{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,30]],"date-time":"2025-08-30T00:06:16Z","timestamp":1756512376235,"version":"3.44.0"},"reference-count":76,"publisher":"Association for Computing Machinery (ACM)","issue":"3","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Evol. Learn. Optim."],"published-print":{"date-parts":[[2025,9,30]]},"abstract":"<jats:p>The exploration\u2013exploitation tradeoff poses a significant challenge in surrogate optimization for expensive black-box functions, particularly when dealing with batch evaluation settings. Despite efforts to develop batch sampling techniques, they often fall short of sufficiently prioritizing diversity within the selected batch. In this article, we propose a fundamentally novel approach called Determinantal Point Processes (DPP)-Based Surrogate Optimization (DPPSO), which serves as a consolidated framework. DPPSO introduces a novel discretization scheme and sampling algorithm that fuses exploration and exploitation objectives by harnessing the power of DPP decomposition. An essential aspect of this project is the development of effective scoring functions to incorporate the quality of the sampled points in the decomposition. We provide theoretical guarantees achieving lower bounds on the probability of convergence. We demonstrate the effectiveness of DPPSO across different benchmarks, comparing its performance against various baseline methods.<\/jats:p>","DOI":"10.1145\/3721296","type":"journal-article","created":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T12:19:39Z","timestamp":1741090779000},"page":"1-30","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Enhancing Batch Diversity in Surrogate Optimization: A Determinantal Point Processes Approach"],"prefix":"10.1145","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1473-6436","authenticated-orcid":false,"given":"Nazanin","family":"Nezami","sequence":"first","affiliation":[{"name":"Department of Mechanical and Industrial Engineering, University of Illinois Chicago, Chicago, IL, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1935-7571","authenticated-orcid":false,"given":"Hadis","family":"Anahideh","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Industrial Engineering, University of Illinois Chicago, Chicago, IL, USA"}]}],"member":"320","published-online":{"date-parts":[[2025,8,29]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2021.105444"},{"key":"e_1_3_2_3_1","first-page":"103","volume-title":"Conference on Learning Theory","author":"Anari Nima","year":"2016","unstructured":"Nima Anari, Shayan Oveis Gharan, and Alireza Rezaei. 2016. Monte Carlo Markov chain algorithms for sampling strongly Rayleigh distributions and determinantal point processes. In Conference on Learning Theory. PMLR, 103\u2013115."},{"key":"e_1_3_2_4_1","first-page":"324","volume-title":"International Conference on Machine Learning","author":"Angermueller Christof","year":"2020","unstructured":"Christof Angermueller, David Belanger, Andreea Gane, Zelda Mariet, David Dohan, Kevin Murphy, Lucy Colwell, and D. Sculley. 2020. Population-based black-box optimization for biological sequence design. In International Conference on Machine Learning. PMLR, 324\u2013334."},{"key":"e_1_3_2_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/040603371"},{"key":"e_1_3_2_6_1","first-page":"21524","article-title":"BoTorch: A framework for efficient Monte-Carlo Bayesian optimization","volume":"33","author":"Balandat Maximilian","year":"2020","unstructured":"Maximilian Balandat, Brian Karrer, Daniel Jiang, Samuel Daulton, Ben Letham, Andrew G. Wilson, and Eytan Bakshy. 2020. BoTorch: A framework for efficient Monte-Carlo Bayesian optimization. Advances in Neural Information Processing Systems 33 (2020), 21524\u201321538.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_7_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.aad2257"},{"key":"e_1_3_2_8_1","unstructured":"Erdem B\u0131y\u0131k Kenneth Wang Nima Anari and Dorsa Sadigh. 2019. Batch active learning using determinantal point processes. arXiv:1906.07975. Retrieved from https:\/\/arxiv.org\/abs\/1906.07975"},{"key":"e_1_3_2_9_1","unstructured":"Alexei Borodin. 2009. Determinantal point processes. arXiv:0911.1153. Retrieved from https:\/\/arxiv.org\/abs\/0911.1153"},{"key":"e_1_3_2_10_1","first-page":"716","volume-title":"International Conference on Machine Learning","author":"Celis Elisa","year":"2018","unstructured":"Elisa Celis, Vijay Keswani, Damian Straszak, Amit Deshpande, Tarun Kathuria, and Nisheeth Vishnoi. 2018. Fair and diverse DPP-based data summarization. In International Conference on Machine Learning. PMLR, 716\u2013725."},{"key":"e_1_3_2_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-44973-4_7"},{"key":"e_1_3_2_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-40988-2_15"},{"key":"e_1_3_2_13_1","first-page":"951","volume-title":"International Conference on Machine Learning","author":"Daxberger Erik A.","year":"2017","unstructured":"Erik A. Daxberger and Bryan Kian Hsiang Low. 2017. Distributed batch Gaussian process optimization. In International Conference on Machine Learning. PMLR, 951\u2013960."},{"key":"e_1_3_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/3425501"},{"key":"e_1_3_2_15_1","doi-asserted-by":"publisher","DOI":"10.5555\/2627435.2750368"},{"key":"e_1_3_2_16_1","unstructured":"David Eriksson David Bindel and Christine A. Shoemaker. 2019a. pySOT and POAP: An event-driven asynchronous framework for surrogate optimization. arXiv:1908.00420. Retrieved from https:\/\/arxiv.org\/abs\/1908.00420"},{"key":"e_1_3_2_17_1","first-page":"5496","article-title":"Scalable global optimization via local Bayesian optimization","volume":"32","author":"Eriksson David","year":"2019","unstructured":"David Eriksson, Michael Pearce, Jacob Gardner, Ryan D. Turner, and Matthias Poloczek. 2019b. Scalable global optimization via local Bayesian optimization. Advances in Neural Information Processing Systems 32 (2019), 5496\u20135507.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_18_1","unstructured":"Peter I. Frazier. 2018. A tutorial on Bayesian optimization. arXiv:1807.02811. Retrieved from https:\/\/arxiv.org\/abs\/1807.02811"},{"key":"e_1_3_2_19_1","doi-asserted-by":"publisher","DOI":"10.1137\/070693424"},{"key":"e_1_3_2_20_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347963"},{"key":"e_1_3_2_21_1","unstructured":"David Ginsbourger Rodolphe Le Riche and Laurent Carraro. 2008. A multi-points criterion for deterministic parallel global optimization based on Gaussian processes. HAL Open Science."},{"key":"e_1_3_2_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-10701-6_6"},{"key":"e_1_3_2_23_1","first-page":"648","volume-title":"Artificial Intelligence and Statistics","author":"Gonz\u00e1lez Javier","year":"2016","unstructured":"Javier Gonz\u00e1lez, Zhenwen Dai, Philipp Hennig, and Neil Lawrence. 2016. Batch Bayesian optimization via local penalization. In Artificial Intelligence and Statistics. PMLR, 648\u2013657."},{"key":"e_1_3_2_24_1","doi-asserted-by":"publisher","DOI":"10.5555\/3546258.3546418"},{"key":"e_1_3_2_25_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-016-1432-3"},{"key":"e_1_3_2_26_1","first-page":"2027","volume-title":"International Conference on Artificial Intelligence and Statistics","author":"Hashimoto Tatsunori","year":"2018","unstructured":"Tatsunori Hashimoto, Steve Yadlowsky, and John Duchi. 2018. Derivative free optimization via repeated classification. In International Conference on Artificial Intelligence and Statistics. PMLR, 2027\u20132036."},{"key":"e_1_3_2_27_1","first-page":"1699","volume-title":"International Conference on Machine Learning","author":"Hern\u00e1ndez-Lobato Jos\u00e9 Miguel","year":"2015","unstructured":"Jos\u00e9 Miguel Hern\u00e1ndez-Lobato, Michael Gelbart, Matthew Hoffman, Ryan Adams, and Zoubin Ghahramani. 2015. Predictive entropy search for Bayesian optimization with unknown constraints. In International Conference on Machine Learning. PMLR, 1699\u20131707."},{"key":"e_1_3_2_28_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v31i1.10647"},{"key":"e_1_3_2_29_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1012771025575"},{"key":"e_1_3_2_30_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00941892"},{"key":"e_1_3_2_31_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008306431147"},{"key":"e_1_3_2_32_1","first-page":"4213","article-title":"Batched Gaussian process bandit optimization via determinantal point processes","volume":"29","author":"Kathuria Tarun","year":"2016","unstructured":"Tarun Kathuria, Amit Deshpande, and Pushmeet Kohli. 2016. Batched Gaussian process bandit optimization via determinantal point processes. Advances in Neural Information Processing Systems 29 (2016), 4213\u20134221.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_33_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-019-01428-7"},{"key":"e_1_3_2_34_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-016-0407-7"},{"key":"e_1_3_2_35_1","first-page":"1171","article-title":"Structured determinantal point processes","volume":"23","author":"Kulesza Alex","year":"2010","unstructured":"Alex Kulesza and Ben Taskar. 2010. Structured determinantal point processes. Advances in Neural Information Processing Systems 23 (2010), 1171\u20131179.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_36_1","doi-asserted-by":"crossref","unstructured":"Alex Kulesza and Ben Taskar. 2012. Determinantal point processes for machine learning. arXiv:1207.6083. Retrieved from https:\/\/arxiv.org\/abs\/1207.6083","DOI":"10.1561\/9781601986290"},{"key":"e_1_3_2_37_1","doi-asserted-by":"crossref","unstructured":"Harold J. Kushner. 1964. A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise. Journal of Basic Engineering 86 1 (March 1964) 97\u2013106.","DOI":"10.1115\/1.3653121"},{"key":"e_1_3_2_38_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492919000060"},{"key":"e_1_3_2_39_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-27926-8_4"},{"key":"e_1_3_2_40_1","doi-asserted-by":"publisher","DOI":"10.1002\/cite.201800091"},{"issue":"235","key":"e_1_3_2_41_1","first-page":"1","article-title":"Gibbon: General-purpose information-based Bayesian optimisation","volume":"22","author":"Moss Henry B.","year":"2021","unstructured":"Henry B. Moss, David S. Leslie, Javier Gonzalez, and Paul Rayson. 2021. Gibbon: General-purpose information-based Bayesian optimisation. Journal of Machine Learning Research 22, 235 (2021), 1\u201349.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_2_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-014-0184-0"},{"key":"e_1_3_2_43_1","first-page":"7031","volume-title":"International Conference on Artificial Intelligence and Statistics","author":"Nava Elvis","year":"2022","unstructured":"Elvis Nava, Mojmir Mutny, and Andreas Krause. 2022. Diversified sampling for batched Bayesian optimization with determinantal point processes. In International Conference on Artificial Intelligence and Statistics. PMLR, 7031\u20137054."},{"key":"e_1_3_2_44_1","doi-asserted-by":"publisher","DOI":"10.1109\/WSC60868.2023.10408315"},{"key":"e_1_3_2_45_1","first-page":"61","volume-title":"European Symposium on the State of the Art in Computational Intelligence","author":"O\u010den\u00e1\u0161ek Ji\u0159\u00ed","year":"2000","unstructured":"Ji\u0159\u00ed O\u010den\u00e1\u0161ek and Josef Schwarz. 2000. The parallel Bayesian optimization algorithm. In European Symposium on the State of the Art in Computational Intelligence. Springer, 61\u201367."},{"key":"e_1_3_2_46_1","first-page":"3868","volume-title":"International Conference on Machine Learning","author":"Oh ChangYong","year":"2018","unstructured":"ChangYong Oh, Efstratios Gavves, and Max Welling. 2018. BOCK: Bayesian optimization with cylindrical kernels. In International Conference on Machine Learning. PMLR, 3868\u20133877."},{"key":"e_1_3_2_47_1","first-page":"29816","article-title":"Batch Bayesian optimisation via density-ratio estimation with guarantees","volume":"35","author":"Oliveira Rafael","year":"2022","unstructured":"Rafael Oliveira, Louis Tiao, and Fabio T. Ramos. 2022. Batch Bayesian optimisation via density-ratio estimation with guarantees. Advances in Neural Information Processing Systems 35 (2022), 29816\u201329829.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/3319619.3326829"},{"key":"e_1_3_2_49_1","doi-asserted-by":"publisher","DOI":"10.5555\/1953048.2078195"},{"key":"e_1_3_2_50_1","unstructured":"Michael J. D. Powell. 1987. Radial basis functions for multivariable interpolation: A review. In Algorithms for Approximation 143\u2013167."},{"key":"e_1_3_2_51_1","first-page":"63","volume-title":"Summer School on Machine Learning","author":"Rasmussen Carl Edward","year":"2003","unstructured":"Carl Edward Rasmussen. 2003. Gaussian processes in machine learning. In Summer School on Machine Learning. Springer, 63\u201371."},{"key":"e_1_3_2_52_1","doi-asserted-by":"publisher","DOI":"10.5555\/1756006.1953029"},{"key":"e_1_3_2_53_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2010.09.013"},{"key":"e_1_3_2_54_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-004-0570-0"},{"key":"e_1_3_2_55_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1060.0182"},{"key":"e_1_3_2_56_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1090.0325"},{"key":"e_1_3_2_57_1","doi-asserted-by":"publisher","DOI":"10.1080\/0305215X.2012.687731"},{"key":"e_1_3_2_58_1","unstructured":"Scikit-Learn-Contrib. 2013. Py-earth: A python implementation of Jerome Friedman\u2019s multivariate adaptive regression splines. Retrieved January 15 2020 from https:\/\/github.com\/scikit-learn-contrib\/py-earth"},{"key":"e_1_3_2_59_1","first-page":"3330","article-title":"Parallel predictive entropy search for batch global optimization of expensive objective functions","volume":"28","author":"Shah Amar","year":"2015","unstructured":"Amar Shah and Zoubin Ghahramani. 2015. Parallel predictive entropy search for batch global optimization of expensive objective functions. Advances in Neural Information Processing Systems 28 (2015), 3330\u20133338.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_60_1","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2015.2494218"},{"key":"e_1_3_2_61_1","first-page":"29","article-title":"Kernel functions for machine learning applications","volume":"3","author":"Souza C\u00e9sar R.","year":"2010","unstructured":"C\u00e9sar R. Souza. 2010. Kernel functions for machine learning applications. Creative Commons Attribution-Noncommercial-Share Alike 3 (2010), 29.","journal-title":"Creative Commons Attribution-Noncommercial-Share Alike"},{"key":"e_1_3_2_62_1","unstructured":"Niranjan Srinivas Andreas Krause Sham M. Kakade and Matthias Seeger. 2009. Gaussian process optimization in the bandit setting: No regret and experimental design. arXiv:0912.3995. Retrieved from https:\/\/arxiv.org\/abs\/0912.3995"},{"key":"e_1_3_2_63_1","doi-asserted-by":"publisher","DOI":"10.5555\/2777421.2777437"},{"key":"e_1_3_2_64_1","volume-title":"Improving Bayesian Optimization for Machine Learning Using Expert Priors","author":"Swersky Kevin","year":"2017","unstructured":"Kevin Swersky. 2017. Improving Bayesian Optimization for Machine Learning Using Expert Priors. University of Toronto (Canada)."},{"key":"e_1_3_2_65_1","doi-asserted-by":"publisher","DOI":"10.1029\/2005WR004723"},{"key":"e_1_3_2_66_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.2019.1966"},{"key":"e_1_3_2_67_1","first-page":"3656","volume-title":"International Conference on Machine Learning","author":"Wang Zi","year":"2017","unstructured":"Zi Wang, Chengtao Li, Stefanie Jegelka, and Pushmeet Kohli. 2017. Batched high-dimensional Bayesian optimization via structural kernel learning. In International Conference on Machine Learning. PMLR, 3656\u20133664."},{"key":"e_1_3_2_68_1","volume-title":"Gaussian Processes for Machine Learning","author":"Williams Christopher K. I.","year":"2006","unstructured":"Christopher K. I. Williams and Carl Edward Rasmussen. 2006. Gaussian Processes for Machine Learning. Vol. 2. MIT Press Cambridge, MA."},{"key":"e_1_3_2_69_1","first-page":"1775","volume-title":"International Conference on Machine Learning","author":"Wilson Andrew","year":"2015","unstructured":"Andrew Wilson, and Hannes Nickisch. 2015. Kernel interpolation for scalable structured gaussian processes (KISS-GP). In International Conference on Machine Learning. PMLR, 1775\u20131784."},{"key":"e_1_3_2_70_1","first-page":"9906","article-title":"Maximizing acquisition functions for Bayesian optimization","volume":"31","author":"Wilson James","year":"2018","unstructured":"James Wilson, Frank Hutter, and Marc Deisenroth. 2018. Maximizing acquisition functions for Bayesian optimization. Advances in Neural Information Processing Systems 31 (2018), 9906\u20139917.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_71_1","unstructured":"James T. Wilson Riccardo Moriconi Frank Hutter and Marc Peter Deisenroth. 2017. The reparameterization trick for acquisition functions. arXiv:1712.00424. Retrieved from https:\/\/arxiv.org\/abs\/1712.00424"},{"key":"e_1_3_2_72_1","doi-asserted-by":"publisher","DOI":"10.1109\/DSAA.2016.12"},{"key":"e_1_3_2_73_1","doi-asserted-by":"publisher","DOI":"10.5555\/959629"},{"key":"e_1_3_2_74_1","first-page":"3134","article-title":"The parallel knowledge gradient method for batch Bayesian optimization","volume":"29","author":"Wu Jian","year":"2016","unstructured":"Jian Wu and Peter Frazier. 2016. The parallel knowledge gradient method for batch Bayesian optimization. Advances in Neural Information Processing Systems 29 (2016), 3134\u20133142.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_75_1","first-page":"5273","article-title":"Bayesian optimization with gradients","volume":"30","author":"Wu Jian","year":"2017","unstructured":"Jian Wu, Matthias Poloczek, Andrew G. Wilson, and Peter Frazier. 2017. Bayesian optimization with gradients. Advances in Neural Information Processing Systems 30 (2017), 5273\u20135284.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_76_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2021.3054811"},{"key":"e_1_3_2_77_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jconhyd.2016.01.004"}],"container-title":["ACM Transactions on Evolutionary Learning and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3721296","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T15:23:17Z","timestamp":1756480997000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3721296"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,29]]},"references-count":76,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,9,30]]}},"alternative-id":["10.1145\/3721296"],"URL":"https:\/\/doi.org\/10.1145\/3721296","relation":{},"ISSN":["2688-3007"],"issn-type":[{"type":"electronic","value":"2688-3007"}],"subject":[],"published":{"date-parts":[[2025,8,29]]},"assertion":[{"value":"2023-11-09","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-02-07","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-08-29","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}