Abstract
In this talk, I will describe a surprising application for a known online learning problem and its optimal algorithm.
First, consider the problem of finding the optimal allocation of money each day to buy stocks at opening prices and sell them at closing prices. We will not assume anything on how the market evolves, yet we would like to be competitive with the fixed allocation strategy, that is, with the optimal rebalanced portfolio in hindsight. This is a classic problem in information theory and it is known to be optimally solved by the Universal Portfolio Algorithm by Cover and Ordentlich (1996).
Now, consider the problem of calculating valid and never vacuous confidence sequences for the unknown expectation of a bounded random variable. Surprisingly, we will show that this problem can also be optimally solved using the Universal Portfolio Algorithm with a market of 2 stocks, where the opening and closing prices depend on the observed outcomes of the random variable. Empirical experiments to show the tightness of the bounds will be shown as well.
Brief Biography
After working as a postdoctoral fellow at the Idiap Research Institute, Switzerland, and the University of Milan, Italy, Professor Francesco Orabona joined the Toyota Technological Institute, Chicago, U.S., as a research assistant professor in 2011.
Following this, he became a senior research scientist at Yahoo Labs, New Jersey, U.S., an assistant professor at Stony Brook University, New York, U.S., and an associate professor at Boston University, U.S
