论文标题
多目标贝叶斯优化中的单卷酸盐与多形酸酯
Mono-surrogate vs Multi-surrogate in Multi-objective Bayesian Optimisation
论文作者
论文摘要
贝叶斯优化（BO）已被广泛用于解决昂贵功能评估的问题。在多目标优化问题中，BO旨在找到一组近似的帕累托最佳解决方案。通常，有两种方法可以通过汇总目标函数（通过使用标量函数（也称为单溶方法方法）和多个替代物（对于每个目标功能，也称为多流形方法），可以通过汇总目标函数来构建替代物：一个替代物。在这两种方法中，都使用采集功能（AF）来指导搜索过程。单溶剂的优势是，仅使用一个模型，但是该方法具有两个主要局限性。首先，标量功能和目标函数的健身景观可能不相似。其次，该方法假定标量函数分布是高斯，因此可以使用AF的闭合形式表达。在这项工作中，我们通过为每个目标函数构建替代模型来克服这些局限性，并表明标量功能分布不是高斯。我们使用广义极值分布近似分布。与标准基准和现实世界优化问题的现有方法的结果和比较表明了多卷酸盐方法的潜力。
Bayesian optimisation (BO) has been widely used to solve problems with expensive function evaluations. In multi-objective optimisation problems, BO aims to find a set of approximated Pareto optimal solutions. There are typically two ways to build surrogates in multi-objective BO: One surrogate by aggregating objective functions (by using a scalarising function, also called mono-surrogate approach) and multiple surrogates (for each objective function, also called multi-surrogate approach). In both approaches, an acquisition function (AF) is used to guide the search process. Mono-surrogate has the advantage that only one model is used, however, the approach has two major limitations. Firstly, the fitness landscape of the scalarising function and the objective functions may not be similar. Secondly, the approach assumes that the scalarising function distribution is Gaussian, and thus a closed-form expression of the AF can be used. In this work, we overcome these limitations by building a surrogate model for each objective function and show that the scalarising function distribution is not Gaussian. We approximate the distribution using Generalised extreme value distribution. The results and comparison with existing approaches on standard benchmark and real-world optimisation problems show the potential of the multi-surrogate approach.
