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A popular approach to tackle such problems is Bayesian optimisation, which builds a response surface model based on the data collected so far, and uses the mean and uncertainty predicted by the model to decide what information to collect next. In this article, we propose a generalisation of the well-known Knowledge Gradient acquisition function that allows it to handle constraints. We empirically compare the new algorithm with four other state-of-the-art constrained Bayesian optimisation algorithms and demonstrate its superior performance. We also prove theoretical convergence in the infinite budget limit.<\/jats:p>","DOI":"10.1145\/3641544","type":"journal-article","created":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T11:55:49Z","timestamp":1705924549000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["Bayesian Optimisation for Constrained Problems"],"prefix":"10.1145","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8091-515X","authenticated-orcid":false,"given":"Juan","family":"Ungredda","sequence":"first","affiliation":[{"name":"Mathematics for Real-World Systems, University of Warwick, Coventry, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4343-5878","authenticated-orcid":false,"given":"Juergen","family":"Branke","sequence":"additional","affiliation":[{"name":"Warwick Business School, University of Warwick, Coventry, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2024,4,8]]},"reference":[{"key":"e_1_3_4_2_1","doi-asserted-by":"publisher","DOI":"10.1561\/2200000036"},{"key":"e_1_3_4_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-015-2019-x"},{"key":"e_1_3_4_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/3071178.3071278"},{"key":"e_1_3_4_5_1","volume-title":"Advances in Neural Information Processing Systems 33","author":"Balandat Maximilian","year":"2020","unstructured":"Maximilian Balandat, Brian Karrer, Daniel R. 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