加速贝叶斯优化中的前瞻：多层蒙特卡洛即你所需
Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Need
AI总结：
利用多层蒙特卡洛（MLMC）解决多步前瞻贝叶斯优化中嵌套期望导致的朴素MC复杂度退化问题，实现标准收敛速率，并在理论与基准实验中验证了其有效性与广泛适用性。
摘要：
我们利用多层蒙特卡洛（MLMC）来提升涉及嵌套期望与最大化的多步前瞻贝叶斯优化（BO）方法的性能。这些期望通常必须通过蒙特卡洛（MC）计算。朴素MC的复杂度速率在嵌套操作时会退化，而MLMC能够针对此类问题实现标准的MC收敛速率，且独立于维度、无需任何平滑性假设。我们的理论研究聚焦于两步和三步前瞻采集函数的近似改进，但正如我们所讨论的，该方法可从多方面推广，包括超越BO的语境。我们的发现通过数值验证，并在多个基准示例中展示了MLMC对BO的益处。代码可在https://github.com/Shangda-Yang/MLMCBO获取。
英文摘要：
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 .
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
