利用最优值上下界信息，提升贝叶斯优化效率
Respecting the limit:Bayesian optimization with a bound on the optimal value
- 引入带约束的高斯过程模型（SlogGP）和改进的期望提升准则
- 在多个基准测试中显著优于传统方法，尤其在已知最优值边界时
- 即使无先验边界信息，也比标准GP表现更好，因其表达能力更强
在许多实际优化问题中，我们对目标函数可达到的取值范围有先验知识。本文研究了已知最小值确切值或可能不精确的下界的情况。提出一种感知边界的贝叶斯优化方法（BABO），采用新的代理模型和采集函数来利用此类先验信息。提出SlogGP代理模型，融入边界信息并相应调整期望提升（EI）采集函数。在多种基准测试上的实验结果表明，考虑最优值先验信息能带来显著收益，且所提方法明显优于现有技术。此外，即使缺乏最优值边界先验，所提SlogGP模型在多数情况下仍优于标准高斯过程模型，这归因于其更强的表达能力。
原文摘要 · Abstract (English)
In many real-world optimization problems, we have prior information about what objective function values are achievable. In this paper, we study the scenario that we have either exact knowledge of the minimum value or a, possibly inexact, lower bound on its value. We propose bound-aware Bayesian optimization (BABO), a Bayesian optimization method that uses a new surrogate model and acquisition function to utilize such prior information. We present SlogGP, a new surrogate model that incorporates bound information and adapts the Expected Improvement (EI) acquisition function accordingly. Empirical results on a variety of benchmarks demonstrate the benefit of taking prior information about the optimal value into account, and that the proposed approach significantly outperforms existing techniques. Furthermore, we notice that even in the absence of prior information on the bound, the proposed SlogGP surrogate model still performs better than the standard GP model in most cases, which we explain by its larger expressiveness.
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