貝葉斯優化是一種尋找黑盒問題最佳解的有效方法，但對於高維問題通常
表現不佳。雖然有很多方法，例如TuRBO (信賴區域的貝葉斯優化) 來解決高
維問題中過度探索，以及高斯過程在高維空間中難以全局逼近真實函數的問
題，但他們仍然可能收斂緩慢或停滯不前。在本文中我們提出了一種新方法
CoMABO (自適應共變異數的貝葉斯優化) 增強TuRBO 的收斂性，自適應共變
異數是一種基於高斯模型採樣點構建共變異數的技術， CoMABO 利用它更佳
的探索候選點並優化複雜的代理模型，實驗結果表明CoMABO 提高了TuRBO
在各種基準問題和實際應用問題中的收斂性。

Bayesian optimization, an effective method for searching the optimal solution of black-box functions, usually performs poorly for high-dimensional problems. Although many methods, such as TuRBO (Trust regions Bayesian optimization), have been proposed to solve the over-emphasis of exploration in high-dimensional global acquisition, they may converge slowly or stagnate. In this paper, we proposed a new method, called CoMABO (Covariance Matrix Adaptation for Bayesian Optimization) to enhance the convergence of TuRBO algorithm. Covariance matrix adaptation is a technique that builds Gaussian models based on the covariance matrix constructed from sampled points. CoMABO utilizes it to explore better candidate points and to optimize the complex surrogate model. Experimental results show CoMABO improves the convergence of TuRBO on various benchmark problems and real world applications.

Abstract (Chinese) 1
Abstract 2
Contents 3
List of Figures 5
List of Tables 6
List of Algorithms 7
1 Introduction 8
2 Related Work 10
3 CoMABO Algorithm 14
3.1 Initial Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Acquisition Function
(Inner Optimization Problem) . . . . . . . . . . . . . . . . . . . . . 16
3.3 Data Augmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 Experiments 19
4.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Test Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2.1 14D Robot pushing . . . . . . . . . . . . . . . . . . . . . . . 20
4.2.2 60D Rover trajectory planning . . . . . . . . . . . . . . . . . 20
4.2.3 200D Ackley function . . . . . . . . . . . . . . . . . . . . . . 21
4.2.4 100D Levy function . . . . . . . . . . . . . . . . . . . . . . . 21
4.3 Experimental Results And Analysis . . . . . . . . . . . . . . . . . . 21
4.4 Different Integration Methods . . . . . . . . . . . . . . . . . . . . . 24
5 Conclusion and future work 29
Bibliography 30
Appendix 35
A Gaussian Process Regression . . . . . . . . . . . . . . . . . . . . . . 35
B CMA-ES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

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