用随机与监督嵌入结合，高效解决高维黑箱优化问题
High-Dimensional Bayesian Optimization Using Both Random and Supervised Embeddings
- 通过自适应学习随机和监督嵌入子空间降低维度
- 在10到600维问题上显著减少仿真调用次数和耗时
- 适合高维昂贵函数优化，尤其适用于工程设计场景
贝叶斯优化（BO）是求解计算成本高昂的黑箱优化问题的强大策略。然而，传统BO方法受限于维数灾难，仅适用于低维问题。本文提出一种高维优化方法，通过引入小维度的线性嵌入子空间实现高效优化，并结合自适应学习策略优化嵌入。所提方法名为高效全局优化耦合随机与监督嵌入（EGORSE），以自适应方式融合随机与监督线性嵌入。在包含10至600个设计变量的学术测试问题上，EGORSE与现有最优算法对比，结果表明其在计算时间与黑箱仿真调用次数方面均表现出显著优势，展现出解决高维黑箱优化问题的巨大潜力。
原文摘要 · Abstract (English)
Bayesian optimization (BO) is one of the most powerful strategies to solve computationally expensive-to-evaluate blackbox optimization problems. However, BO methods are conventionally used for optimization problems of small dimension because of the curse of dimensionality. In this paper, a high-dimensionnal optimization method incorporating linear embedding subspaces of small dimension is proposed to efficiently perform the optimization. An adaptive learning strategy for these linear embeddings is carried out in conjunction with the optimization. The resulting BO method, named efficient global optimization coupled with random and supervised embedding (EGORSE), combines in an adaptive way both random and supervised linear embeddings. EGORSE has been compared to state-of-the-art algorithms and tested on academic examples with a number of design variables ranging from 10 to 600. The obtained results show the high potential of EGORSE to solve high-dimensional blackbox optimization problems, in terms of both CPU time and the limited number of calls to the expensive blackbox simulation.
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