arXiv Open Access 2024

Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Need

Shangda Yang Vitaly Zankin Maximilian Balandat Stefan Scherer Kevin Carlberg +2 lainnya

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Abstrak

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 .

Topik & Kata Kunci

stat.ML cs.LG math.OC math.PR stat.CO stat.ME

Penulis (7)

Shangda Yang

Vitaly Zankin

Maximilian Balandat

Stefan Scherer

Kevin Carlberg

Neil Walton

Kody J. H. Law

Format Sitasi

APA MLA BibTeX

Yang, S., Zankin, V., Balandat, M., Scherer, S., Carlberg, K., Walton, N. et al. (2024). Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Need. https://arxiv.org/abs/2402.02111

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓