High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two stages. First, we take samples following a sparse grid experimental design and approximate the response surface via kernel ridge regression with a Brownian field kernel. Second, we follow the expected improvement strategy -- with critical modifications that boost the algorithm's sample efficiency -- to iteratively sample from the next level of the sparse grid. Under mild conditions on the smoothness of the response surface and the simulation noise, we establish upper bounds on the convergence rate for both noise-free and noisy simulation samples. These upper bounds deteriorate only slightly in the dimension of the feasible set, and they can be improved if the objective function is known to be of a higher-order smoothness. Extensive numerical experiments demonstrate that the proposed algorithm dramatically outperforms typical alternatives in practice.

翻译：高维模拟优化具有众所周知的挑战性。 我们提出一种新的取样算法, 与全球最佳解决方案相融合, 且受维度诅咒的影响最小。 算法由两个阶段组成。 首先, 我们根据一个稀疏的网格实验设计采集样本, 并用布朗的野外内核来接近反应表面。 其次, 我们遵循预期的改进战略, 并进行重大修改, 提高算法的样本效率, 以从稀疏格中迭接为样本。 在反应表面和模拟噪音的平滑性等温和条件下, 我们对无噪音和吵闹模拟样品的趋同率设定了上限。 这些上限线在可行的一组样本中只是略微恶化, 如果已知客观功能是更高层次的顺畅度, 可以改进它们。 广泛的数字实验表明, 拟议的算法在实际中大大优于典型的替代方法。