Consider three problems: universal data compression, online portfolio selection, and learning quantum states. Despite their very different application scenarios, the three problems share similar mathematical structures. Among them, online portfolio selection has been a famous open problem in online learning for more than 30 years; learning quantum states is a generalization of it and hence even more challenging. Recently, there have been interesting breakthroughs. In this talks, I will give an overview of the problems and recent breakthroughs.
I am an assistant professor at the Department of Computer Science and Information Engineering, National Taiwan University. I work on the design and analyses of machine learning and optimization algorithms. I am particularly interested in decision making under uncertainty, without strong assumptions on the reality. My research fields include machine learning, mathematical statistics, convex optimization, and quantum information.