{"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-under-heavy-tailed","title":"Bayesian Optimization under Heavy-tailed Payoffs","arxiv_id":"1909.07040","date":"2019-09-16","proceeding":"NeurIPS 2019 12","authors":["Sayak Ray Chowdhury","Aditya Gopalan"],"abstract":"We consider black box optimization of an unknown function in the nonparametric Gaussian process setting when the noise in the observed function values can be heavy tailed. This is in contrast to existing literature that typically assumes sub-Gaussian noise distributions for queries. Under the assumption that the unknown function belongs to the Reproducing Kernel Hilbert Space (RKHS) induced by a kernel, we first show that an adaptation of the well-known GP-UCB algorithm with reward truncation enjoys sublinear $\\tilde{O}(T^{\\frac{2 + \\alpha}{2(1+\\alpha)}})$ regret even with only the $(1+\\alpha)$-th moments, $\\alpha \\in (0,1]$, of the reward distribution being bounded ($\\tilde{O}$ hides logarithmic factors). However, for the common squared exponential (SE) and Mat\\'{e}rn kernels, this is seen to be significantly larger than a fundamental $\\Omega(T^{\\frac{1}{1+\\alpha}})$ lower bound on regret. We resolve this gap by developing novel Bayesian optimization algorithms, based on kernel approximation techniques, with regret bounds matching the lower bound in order for the SE kernel. We numerically benchmark the algorithms on environments based on both synthetic models and real-world data sets.","url_abs":"https://arxiv.org/abs/1909.07040v1","url_pdf":"https://arxiv.org/pdf/1909.07040v1.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-under-heavy-tailed","repo_url":"https://github.com/sayakrc/Bayesian-Optimization-under-Heavy-tailed-Payoffs","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"bayesian-optimization","task_name":"Bayesian Optimization"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1909.07040","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}