{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/dealing-with-integer-valued-variables-in","title":"Dealing with Integer-valued Variables in Bayesian Optimization with Gaussian Processes","arxiv_id":"1706.03673","date":"2017-06-12","proceeding":null,"authors":["Eduardo C. Garrido-Merchán","Daniel Hernández-Lobato"],"abstract":"Bayesian optimization (BO) methods are useful for optimizing functions that\nare expensive to evaluate, lack an analytical expression and whose evaluations\ncan be contaminated by noise. These methods rely on a probabilistic model of\nthe objective function, typically a Gaussian process (GP), upon which an\nacquisition function is built. This function guides the optimization process\nand measures the expected utility of performing an evaluation of the objective\nat a new point. GPs assume continous input variables. When this is not the\ncase, such as when some of the input variables take integer values, one has to\nintroduce extra approximations. A common approach is to round the suggested\nvariable value to the closest integer before doing the evaluation of the\nobjective. We show that this can lead to problems in the optimization process\nand describe a more principled approach to account for input variables that are\ninteger-valued. We illustrate in both synthetic and a real experiments the\nutility of our approach, which significantly improves the results of standard\nBO methods on problems involving integer-valued variables.","url_abs":"http://arxiv.org/abs/1706.03673v2","url_pdf":"http://arxiv.org/pdf/1706.03673v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"dealing-with-integer-valued-variables-in","repo_url":"https://github.com/darthdeus/master-thesis-code","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"bayesian-optimization","task_name":"Bayesian Optimization"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.03673","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}