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In this paper we associate the inputs to discrete probability distributions which are elements of the probability simplex. To search in the new design space, we need a distance between distributions. The optimal transport distance (aka Wasserstein distance) is chosen due to its mathematical structure and the computational strategies enabled by it. Both the GP and the acquisition function is generalized to an acquisition functional over the probability simplex. To optimize this functional two methods are proposed, one based on auto differentiation and the other based on proximal-point algorithm and the gradient flow. Finally, we report a preliminary set of computational results on a class of problems whose dimension ranges from 5 to 100. These results show that embedding the Bayesian optimization process in the probability simplex enables an effective algorithm whose performance over standard Bayesian optimization improves with the increase of problem dimensionality.<\/jats:p>","DOI":"10.1007\/s10472-023-09883-w","type":"journal-article","created":{"date-parts":[[2023,7,18]],"date-time":"2023-07-18T05:01:43Z","timestamp":1689656503000},"page":"77-91","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bayesian optimization over the probability simplex"],"prefix":"10.1007","volume":"93","author":[{"given":"Antonio","family":"Candelieri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4187-4209","authenticated-orcid":false,"given":"Andrea","family":"Ponti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Archetti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,7,18]]},"reference":[{"key":"9883_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-24494-1","volume-title":"Bayesian optimization and data science","author":"F Archetti","year":"2019","unstructured":"Archetti, F., Candelieri, A.: Bayesian optimization and data science. 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The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit\u00a0.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest statement"}}]}}