- 學位論文
高維度貝式最佳化之縮小範圍選點
High Dimensional Bayesian Optimization Via Narrow Down Parameter Space
摘要
貝式最佳化常被用來解決昂貴的黑盒函數，逐次找出使目標函數達到最佳的參數點，而傳統離散型的貝式最佳化會受參數空間的維度限制以致於無法在高維度上運用，且大部分的高維度貝式最佳化皆會對目標函數做額外的假設來達成降維的效果。為此本研究將目標更改為在最少迭代次數下，找到使目標函數達到最佳值的80% ~ 90% 的次佳參數點，並提出一個不需要做額外的假設的方法縮小範圍選點，在結合徵用函數與參數空間上均勻生成參數點的概念，使得在任何目標函數上都能具有穩健性，並討論在各種徵用函數與核函數的影響下，去挑選出最適合的搭配方式。最後透過模擬的方式也證明了此方法具有穩健性，也能在尚可接受的迭代次數下達成我們的目標，且在相同的迭代次數下，此方法找到的最佳值是顯著大於目前高維度貝式最佳化的基準 方法。
並列摘要
Bayesian Optimization (BO) is usually used to solve the expensive black-box function, and sequentially find the best parameters setting to maximize the objective function. But it is still challenging to extend traditional BO to high dimensional by constrain of parameter space. And most high dimensional BO will make some assumption on objective function to reduce dimension. Therefore in this study, we change our target to find the parameters setting that achieve the maximum’s 80% ~ 90%, and propose a method Narrow Down Parameter Space that don’t need to make any assumption. This method is robust to any objective function by combining acquisition function, and the concept of uniformly generating searching points on parameter space. Moreover, we discuss the effect on many acquisition function and kernel function, then choose the best way. Finally we prove this method is robust and can achieve our target at acceptable iterations via simulations. And the best value found by this method is significant lager than the baseline of high dimensional BO at the same iteration.