AI-Driven Database Tuning: Faster Index Selection with IA2 and TD3-TD-SWAR

Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Related Works Convex Relaxation Techniques for Hyperbolic SVMs 3.1 Preliminaries 3.2 Original Formulation of the HSVM 3.3 Semidefinite Formulation 3.4 Moment-Sum-of-Squares Relaxation Experiments 4.1 Synthetic Dataset 4.2 Real Dataset Discussions, Acknowledgements, and References Related Works Related Works Related Works Convex Relaxation Techniques for Hyperbolic SVMs 3.1 Preliminaries 3.2 Original Formulation of the HSVM 3.3 Semidefinite Formulation 3.4 Moment-Sum-of-Squares Relaxation Convex Relaxation Techniques for Hyperbolic SVMs 3.1 Preliminaries 3.1 Preliminaries 3.2 Original Formulation of the HSVM 3.2 Original Formulation of the HSVM 3.3 Semidefinite Formulation 3.3 Semidefinite Formulation 3.4 Moment-Sum-of-Squares Relaxation 3.4 Moment-Sum-of-Squares Relaxation Experiments 4.1 Synthetic Dataset 4.2 Real Dataset Experiments Experiments 4.1 Synthetic Dataset 4.1 Synthetic Dataset 4.2 Real Dataset 4.2 Real Dataset Discussions, Acknowledgements, and References Discussions, Acknowledgements, and References Discussions, Acknowledgements, and References A. Proofs A. Proofs B. Solution Extraction in Relaxed Formulation B. Solution Extraction in Relaxed Formulation C. On Moment Sum-of-Squares Relaxation Hierarchy C. On Moment Sum-of-Squares Relaxation Hierarchy D. Platt Scaling [31] D. Platt Scaling [31] E. Detailed Experimental Results E. Detailed Experimental Results F. Robust Hyperbolic Support Vector Machine F. Robust Hyperbolic Support Vector Machine 3 Convex Relaxation Techniques for Hyperbolic SVMs In this section, we first introduce fundamentals on hyperbolic spaces and the original formulation of the hyperbolic Support Vector Machine (HSVM) due to Cho et al. [4]. Next, we present two relaxations techniques, the semidefinite relaxation and the moment-sum-of-squares relaxation, that can be solved efficiently with convergence guarantees. Our discussions center on the Lorentz manifold as the choice of hyperbolic space, since it has been shown in Mishne et al. [6] that the Lorentz formulation offers greater numerical advantages in optimization. 3.1 Preliminaries Authors: (1) Sheng Yang, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA (shengyang@g.harvard.edu); (2) Peihan Liu, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA (peihanliu@fas.harvard.edu); (3) Cengiz Pehlevan, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, Center for Brain Science, Harvard University, Cambridge, MA, and Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University, Cambridge, MA (cpehlevan@seas.harvard.edu). Authors: Authors: (1) Sheng Yang, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA (shengyang@g.harvard.edu); (2) Peihan Liu, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA (peihanliu@fas.harvard.edu); (3) Cengiz Pehlevan, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, Center for Brain Science, Harvard University, Cambridge, MA, and Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University, Cambridge, MA (cpehlevan@seas.harvard.edu). This paper is available on arxiv under CC by-SA 4.0 Deed (Attribution-Sharealike 4.0 International) license. This paper is available on arxiv under CC by-SA 4.0 Deed (Attribution-Sharealike 4.0 International) license. available on arxiv available on arxiv