【摘要】 个性化优化是求解含环境变量优化问题的新策略.针对带噪声黑盒函数,我们提出了实现个性化优化的序贯算法.我们首先利用初始设计,建立带噪声的高斯过程模型作为黑盒函数的统计代理模型.基于代理模型,我们提出了一个新的采集函数——分层期望分位数改进(HEQI),通过最大化HEQI得到控制变量的下一个试验点.环境变量的下一个试验点通过优化空间填充准则得到.序贯地执行以上步骤,可以逼近个性化优化的解.一系列数值实验表明,采用HEQI的个性化优化算法在不同的噪声水平下表现都优于采用其他贝叶斯优化策略的算法.更多还原

【Abstract】 Personalized optimization is a new strategy for optimization problems with environmental variables. For noisy black-box functions, this paper proposes a sequential algorithm to implement personalized optimization. We first use an initial design to build a noisy Gaussian process model as the statistical surrogate model of the black-box function. Based on the surrogate model, we introduce a new acquisition function, called hierarchical expected quantile improvement(HEQI), and give the next trial site of the control variables through maximizing HEQI. The next trial site of the environmental variables is obtained via a space-filling criterion. Conducting the above steps sequentially, we can approach the solution of the personalized optimization problem. A number of numerical experiments indicate that the HEQI-based personalized optimization algorithm outperforms those based on other Bayesian optimization strategies at various levels of noise.更多还原