{"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/pareto-active-learning-with-gaussian","title":"Beyond Grids: Multi-objective Bayesian Optimization With Adaptive Discretization","arxiv_id":"2006.14061","date":"2020-06-24","proceeding":null,"authors":["Andi Nika","Sepehr Elahi","Çağın Ararat","Cem Tekin"],"abstract":"We consider the problem of optimizing a vector-valued objective function $\\boldsymbol{f}$ sampled from a Gaussian Process (GP) whose index set is a well-behaved, compact metric space $({\\cal X},d)$ of designs. We assume that $\\boldsymbol{f}$ is not known beforehand and that evaluating $\\boldsymbol{f}$ at design $x$ results in a noisy observation of $\\boldsymbol{f}(x)$. Since identifying the Pareto optimal designs via exhaustive search is infeasible when the cardinality of ${\\cal X}$ is large, we propose an algorithm, called Adaptive $\\boldsymbol{\\epsilon}$-PAL, that exploits the smoothness of the GP-sampled function and the structure of $({\\cal X},d)$ to learn fast. In essence, Adaptive $\\boldsymbol{\\epsilon}$-PAL employs a tree-based adaptive discretization technique to identify an $\\boldsymbol{\\epsilon}$-accurate Pareto set of designs in as few evaluations as possible. We provide both information-type and metric dimension-type bounds on the sample complexity of $\\boldsymbol{\\epsilon}$-accurate Pareto set identification. We also experimentally show that our algorithm outperforms other Pareto set identification methods.","url_abs":"https://arxiv.org/abs/2006.14061v3","url_pdf":"https://arxiv.org/pdf/2006.14061v3.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":"pareto-active-learning-with-gaussian","repo_url":"https://github.com/kerembozgann/adaptive-epsilon-pal","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"active-learning","task_name":"Active Learning"},{"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":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}