{"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-over-hybrid-spaces","title":"Bayesian Optimization over Hybrid Spaces","arxiv_id":"2106.04682","date":"2021-06-08","proceeding":null,"authors":["Aryan Deshwal","Syrine Belakaria","Janardhan Rao Doppa"],"abstract":"We consider the problem of optimizing hybrid structures (mixture of discrete and continuous input variables) via expensive black-box function evaluations. This problem arises in many real-world applications. For example, in materials design optimization via lab experiments, discrete and continuous variables correspond to the presence/absence of primitive elements and their relative concentrations respectively. The key challenge is to accurately model the complex interactions between discrete and continuous variables. In this paper, we propose a novel approach referred as Hybrid Bayesian Optimization (HyBO) by utilizing diffusion kernels, which are naturally defined over continuous and discrete variables. We develop a principled approach for constructing diffusion kernels over hybrid spaces by utilizing the additive kernel formulation, which allows additive interactions of all orders in a tractable manner. We theoretically analyze the modeling strength of additive hybrid kernels and prove that it has the universal approximation property. Our experiments on synthetic and six diverse real-world benchmarks show that HyBO significantly outperforms the state-of-the-art methods.","url_abs":"https://arxiv.org/abs/2106.04682v1","url_pdf":"https://arxiv.org/pdf/2106.04682v1.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-over-hybrid-spaces","repo_url":"https://github.com/aryandeshwal/HyBO","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"bayesian-optimization","task_name":"Bayesian Optimization"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2106.04682","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}