{"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/accelerating-look-ahead-in-bayesian","title":"Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Need","arxiv_id":"2402.02111","date":"2024-02-03","proceeding":null,"authors":["Shangda Yang","Vitaly Zankin","Maximilian Balandat","Stefan Scherer","Kevin Carlberg","Neil Walton","Kody J. H. Law"],"abstract":"We leverage multilevel Monte Carlo (MLMC) to improve the performance of multi-step look-ahead Bayesian optimization (BO) methods that involve nested expectations and maximizations. Often these expectations must be computed by Monte Carlo (MC). The complexity rate of naive MC degrades for nested operations, whereas MLMC is capable of achieving the canonical MC convergence rate for this type of problem, independently of dimension and without any smoothness assumptions. Our theoretical study focuses on the approximation improvements for twoand three-step look-ahead acquisition functions, but, as we discuss, the approach is generalizable in various ways, including beyond the context of BO. Our findings are verified numerically and the benefits of MLMC for BO are illustrated on several benchmark examples. Code is available at https://github.com/Shangda-Yang/MLMCBO .","url_abs":"https://arxiv.org/abs/2402.02111v2","url_pdf":"https://arxiv.org/pdf/2402.02111v2.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":"accelerating-look-ahead-in-bayesian","repo_url":"https://github.com/shangda-yang/mlmcbo","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"all","task_name":"All"},{"task_slug":"bayesian-optimization","task_name":"Bayesian Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2402.02111","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2402.02111"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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