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.

翻译：我们在信任域框架内开发并分析了一种基于高斯过程模型的随机仿真优化方法。本文重点研究目标函数方差较大的场景，此类场景下精确估计具有挑战性且通常需要大量评估。针对该问题域，我们将局部建模与自适应复制相结合，使方法能够在最有利的位置分配重复评估。我们提出了若干促进和调整复制的机制，包括对采集函数的改进和成本感知的评估策略。当需要高水平采样以降低噪声时，这些组件使我们的方法能够有效扩展。数值实验表明，在考虑评估成本的情况下，自适应复制相较于基线方法可将求解精度提升数个数量级，并显著提高计算效率。