论文标题
R-MBO:一种多形的偏好掺入多目标贝叶斯优化的方法
R-MBO: A Multi-surrogate Approach for Preference Incorporation in Multi-objective Bayesian Optimisation
论文作者
论文摘要
许多现实世界中的多目标优化问题依赖于计算昂贵的功能评估。多目标贝叶斯优化(BO)可用于减轻计算时间,以找到一组近似的帕累托最佳解决方案。在许多现实世界中,决策者对目标功能有一些偏好。将偏好纳入多目标BO中的一种方法是在其上使用标量函数并在其上构建单个替代模型(单溶方法)。这种方法有两个主要局限性。首先,标量功能和目标函数的健身景观可能不相似。其次,该方法假设标量函数分布是高斯,因此可以使用采集函数的闭合形式表达,例如,可以使用预期的改进。我们通过在每个目标函数上构建独立的替代模型(多形方法)来克服这些局限性,并表明标量函数的分布不是高斯。我们使用广义价值分布近似分布。我们提出了一种A-PRIORI多形酸酯方法,以将所需的目标函数值(或参考点)纳入多目标BO中的决策者的偏好。与基准和现实世界优化问题上现有的单溶方法的结果和比较表明了拟议方法的潜力。
Many real-world multi-objective optimisation problems rely on computationally expensive function evaluations. Multi-objective Bayesian optimisation (BO) can be used to alleviate the computation time to find an approximated set of Pareto optimal solutions. In many real-world problems, a decision-maker has some preferences on the objective functions. One approach to incorporate the preferences in multi-objective BO is to use a scalarising function and build a single surrogate model (mono-surrogate approach) on it. This 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 an acquisition function e.g., expected improvement can be used. We overcome these limitations by building independent surrogate models (multi-surrogate approach) on each objective function and show that the distribution of the scalarising function is not Gaussian. We approximate the distribution using Generalised value distribution. We present an a-priori multi-surrogate approach to incorporate the desirable objective function values (or reference point) as the preferences of a decision-maker in multi-objective BO. The results and comparison with the existing mono-surrogate approach on benchmark and real-world optimisation problems show the potential of the proposed approach.