Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functions

arXiv:2504.20527v2 Announce Type: replace-cross
Abstract: We develop and analyze a method for stochastic simulation optimization based on Gaussian process models within a trust-region framework. We focus on settings where the variance of the objective function is large, making accurate estimation challenging and often requiring many evaluations. To address this regime, we combine local modeling with adaptive replication, allowing the method to allocate repeated evaluations where they are most beneficial. We introduce several mechanisms to promote and adapt replication, including modifications to the acquisition function and cost-aware evaluation strategies. These components enable our approach to scale effectively when high levels of sampling are required to reduce noise. Numerical experiments show that adaptive replication can substantially improve solution accuracy by several orders of magnitude over baseline methods and computational efficiency when evaluation costs are taken into account.