mlsanityData to 7 Oct 2026

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

arXiv 2402.02111 ↗First posted 3 Feb 2024stat.ML cs.LG math.OCcited by 4

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Abstract (arXiv)

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 .

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 20 of its 64 references that are in the map. First posted on arXiv 3 Feb 2024.

Builds on

20 of 64 references.

References · 20

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8 more
  1. 2021Multi-Step Budgeted Bayesian Optimization with Unknown Evaluation Costscited by 18
  2. 2013On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoodscited by 16
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Cited by year

Citing papers per year: 2024: 1; 2025: 3.

4 papers.

  1. 2024Monte Carlo Tree Search based Space Transfer for Black-box Optimizationcited by 7
  2. 2025Nested Expectations with Kernel Quadraturecited by 5
  3. 2025Multilevel neural simulation-based inferencecited by 5
  4. 2025Generalization and Optimization of SGD with Lookaheadcited by 0