{"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/bayesian-optimization-with-expensive","title":"Bayesian Optimization with Expensive Integrands","arxiv_id":"1803.08661","date":"2018-03-23","proceeding":null,"authors":["Saul Toscano-Palmerin","Peter I. Frazier"],"abstract":"We propose a Bayesian optimization algorithm for objective functions that are\nsums or integrals of expensive-to-evaluate functions, allowing noisy\nevaluations. These objective functions arise in multi-task Bayesian\noptimization for tuning machine learning hyperparameters, optimization via\nsimulation, and sequential design of experiments with random environmental\nconditions. Our method is average-case optimal by construction when a single\nevaluation of the integrand remains within our evaluation budget. Achieving\nthis one-step optimality requires solving a challenging value of information\noptimization problem, for which we provide a novel efficient\ndiscretization-free computational method. We also provide consistency proofs\nfor our method in both continuum and discrete finite domains for objective\nfunctions that are sums. In numerical experiments comparing against previous\nstate-of-the-art methods, including those that also leverage sum or integral\nstructure, our method performs as well or better across a wide range of\nproblems and offers significant improvements when evaluations are noisy or the\nintegrand varies smoothly in the integrated variables.","url_abs":"http://arxiv.org/abs/1803.08661v1","url_pdf":"http://arxiv.org/pdf/1803.08661v1.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":"bayesian-optimization-with-expensive","repo_url":"https://github.com/toscanosaul/bayesian_quadrature_optimization","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"bayesian-optimization","task_name":"Bayesian Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1803.08661","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}