提出新方法提升高维贝叶斯优化的寻优效率
Regional Expected Improvement for Efficient Trust Region Selection in High-Dimensional Bayesian Optimization
- 设计区域期望改进函数，自动识别全局最优可能区域
- 在中高维真实问题上优于传统贝叶斯优化方法
- 无需假设问题特性，适合复杂高维优化场景
现实优化问题常涉及评估成本高的复杂目标函数。尽管基于高斯过程的贝叶斯优化（BO）对此类问题有效，但在高维空间中因评估次数有限而性能下降。现有简化方法如降维依赖特定问题假设，若假设不成立则表现不佳。基于信任域的方法虽避免此类假设，但易陷入局部最优。本文提出新型采集函数——区域期望改进（REI），用于提升中高维场景下的信任域贝叶斯优化性能。REI 能识别可能包含全局最优的区域，不依赖特定问题特征。我们提供了理论证明，表明 REI 可有效确定最优信任区域，并通过实证表明，将 REI 嵌入信任域方法后，在中高维真实问题上优于传统贝叶斯优化及其他高维优化方法。
原文摘要 · Abstract (English)
Real-world optimization problems often involve complex objective functions with costly evaluations. While Bayesian optimization (BO) with Gaussian processes is effective for these challenges, it suffers in high-dimensional spaces due to performance degradation from limited function evaluations. To overcome this, simplification techniques like dimensionality reduction have been employed, yet they often rely on assumptions about the problem characteristics, potentially underperforming when these assumptions do not hold. Trust-region-based methods, which avoid such assumptions, focus on local search but risk stagnation in local optima. In this study, we propose a novel acquisition function, regional expected improvement (REI), designed to enhance trust-region-based BO in medium to high-dimensional settings. REI identifies regions likely to contain the global optimum, improving performance without relying on specific problem characteristics. We provide a theoretical proof that REI effectively identifies optimal trust regions and empirically demonstrate that incorporating REI into trust-region-based BO outperforms conventional BO and other high-dimensional BO methods in medium to high-dimensional real-world problems.
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