Accelerating look-ahead in Bayesian optimization: Multilevel Monte Carlo is all you need

Abstract

We propose a multilevel Monte Carlo approach for accelerating look-ahead strategies in Bayesian optimization. Look-ahead acquisition functions, which consider multiple future evaluations, can significantly improve optimization performance but are computationally expensive to evaluate. Our method leverages the multilevel Monte Carlo framework to efficiently estimate these acquisition functions by combining cheap low-fidelity and expensive high-fidelity evaluations. This approach enables practical use of sophisticated look-ahead strategies that were previously computationally prohibitive.