A new acquisition function for Bayesian optimization based on the moment-generating function
A new acquisition function for Bayesian optimization based on the moment-generating function
复制标题
基于矩生成函数的贝叶斯优化新获取函数
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Thomas Bäck
中科院分区：
文献类型：
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作者：
Hao Wang;Bas van Stein;M. Emmerich;Thomas Bäck
贝叶斯优化或高效全局优化(EGO)是一种针对昂贵的黑盒函数而设计的全局搜索策略。在该算法中，对一些初始数据样本建立统计模型(通常为高斯过程模型)。通过迭代最大化一个所谓的获取函数来逼近全局最优解，该函数平衡了搜索的探索和开发效果。这种算法的性能在很大程度上受捕获函数的选择影响。受高斯过程模型高阶矩的启发，基于改进的矩母函数(MGF)构造了一种新的捕获函数，即通过在未知点采样获得当前最佳适应值的随机增益。这种基于MGF的获取函数考虑了所有的高阶矩，并引入了一个额外的实值参数来控制勘探和开发之间的权衡。文中详细讨论了该函数的动因、理论基础和闭合表达式。此外，我们还说明了它相对于其他捕获函数的优势，特别是所谓的广义预期改进。
Bayesian Optimization or Efficient Global Optimization (EGO) is a global search strategy that is designed for expensive black-box functions. In this algorithm, a statistical model (usually the Gaussian process model) is constructed on some initial data samples. The global optimum is approached by iteratively maximizing a so-called acquisition function, that balances the exploration and exploitation effect of the search. The performance of such an algorithm is largely affected by the choice of the acquisition function. Inspired by the usage of higher moments from the Gaussian process model, it is proposed to construct a novel acquisition function based on the moment-generating function (MGF) of the improvement, which is the stochastic gain over the current best fitness value by sampling at an unknown point. This MGF-based acquisition function takes all the higher moments into account and introduces an additional real-valued parameter to control the trade-off between exploration and exploitation. The motivation, rationale and closed-form expression of the proposed function are discussed in detail. In addition, we also illustrate its advantage over other acquisition functions, especially the so-called generalized expected improvement.
DOI：
10.1007/978-3-642-34413-8_5
发表时间：
2012-01
期刊：
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影响因子：
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作者：
F. Hutter;H. Hoos;Kevin Leyton-Brown
通讯作者：
F. Hutter;H. Hoos;Kevin Leyton-Brown