臺灣博碩士論文加值系統

摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1 Bayesian Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Regret Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4 Multi-Objective Time-Varying Bayesian Optimization . . . . . . . . . . . . . . . 8
4.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.2 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.3 Posterior Updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5 Regret Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.1 Lower Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.1.1 One objective function changes . . . . . . . . . . . . . . . . . . . . . 15
5.1.2 N objective functions change . . . . . . . . . . . . . . . . . . . . . . . 18
5.2 Upper Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2.1 Proof of (5.43) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2.2 Proof of (5.44) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.1 Synthetic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.2 Real-World Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Appendix A Analysis of Mutual Information . . . . . . . . . . . . . . . . . . . . . . 38
Appendix B Main Results to Specific Kernels (Corollary 3) . . . . . . . . . . . . . 42

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