论文标题
高维大规模优化的模型聚合方法
A model aggregation approach for high-dimensional large-scale optimization
论文作者
论文摘要
贝叶斯优化(BO)已被广泛用于机器学习和仿真优化。随着这些领域的计算资源和存储能力的提高,高维和大规模问题变得越来越普遍。在这项研究中,我们在贝叶斯优化(MAMBO)算法中提出了一种模型聚合方法,以有效地解决高维大规模优化问题。 Mambo结合使用亚采样和子空间嵌入来共同解决高维度和大规模问题。此外,采用模型聚合方法来解决应用嵌入时出现的替代模型不确定性问题。在嵌入文献和实践中,这种替代模型不确定性问题在很大程度上被忽略了,并且当问题是高度的,并且数据受到限制时会加剧。我们提出的模型聚合方法降低了这些低维替代模型的风险,并改善了BO算法的鲁棒性。我们得出了针对所提出的聚合替代模型的渐近造成的结合,并证明了Mambo的收敛性。基准数值实验表明,我们的算法与其他常用的高维BO算法相比具有出色或可比的性能。此外,我们将Mambo应用于机器学习算法的级联分类器进行面部检测,结果表明,Mambo发现的设置比基准设置更高,并且在计算上比其他高维BO算法更快。
Bayesian optimization (BO) has been widely used in machine learning and simulation optimization. With the increase in computational resources and storage capacities in these fields, high-dimensional and large-scale problems are becoming increasingly common. In this study, we propose a model aggregation method in the Bayesian optimization (MamBO) algorithm for efficiently solving high-dimensional large-scale optimization problems. MamBO uses a combination of subsampling and subspace embeddings to collectively address high dimensionality and large-scale issues; in addition, a model aggregation method is employed to address the surrogate model uncertainty issue that arises when embedding is applied. This surrogate model uncertainty issue is largely ignored in the embedding literature and practice, and it is exacerbated when the problem is high-dimensional and data are limited. Our proposed model aggregation method reduces these lower-dimensional surrogate model risks and improves the robustness of the BO algorithm. We derive an asymptotic bound for the proposed aggregated surrogate model and prove the convergence of MamBO. Benchmark numerical experiments indicate that our algorithm achieves superior or comparable performance to other commonly used high-dimensional BO algorithms. Moreover, we apply MamBO to a cascade classifier of a machine learning algorithm for face detection, and the results reveal that MamBO finds settings that achieve higher classification accuracy than the benchmark settings and is computationally faster than other high-dimensional BO algorithms.