PREDICTABLE SEQUENCES AND COMPETING WITH STRATEGIES

It seems like yesterday that I arrived on the beautiful campus of the University of Pennsylvania, and it is hard to believe that four wonderful years have already passed. With memories everywhere across the campus, I owe thanks to many people in many ways. I would like to express my deepest appreciation to all of my wonderful profes-sors. Thanks to Professor Charles L. Epstein for accepting me to The Graduate Group in Applied Mathematics and Computational Science (AMCS). That marked the beginning of all the memories. Thanks also to Professor Abraham J. Wyner for introducing me to the field of statistics and to the Wharton Statistics Department and many interesting projects. I would also like to extend my appreciation to Pro-fessor Alexander Rakhlin for introducing me to the field of online learning, and for his support and encouragement throughout my research. Karthik Sridharan offered many brilliant and inspiring ideas, and contributed greatly to my research. Profes-sor Dean Foster served on my thesis committee, and provided extremely valuable career advice. Many thanks, as well, to all of the great professors who instructed me during my twenty courses at Penn. I could not have completed this program without the generous financial support of several professors and departments at the University of Pennsylvania. Thank