Data-Driven Decision Processes - Whiteboard Talk

Title: Data Compression, Gambling and Online Portfolio Selection: A Tutorial

Abstract: In this talk, we will study the problem of sequential portfolio selection: An investor on each day chooses how to divide her wealth so as to invest in m stocks based on the observed performance of each stock so far; the goal is to attain as large a wealth as possible after repeated investments at the end of n days. We will show that the Universal Portfolios method of Cover (1991) is the optimal solution to this problem. To this end, we will also study the classic information theoretic problem of data compression (sometimes also called sequential prediction under the log-loss), show its equivalence to gambling and portfolio selection, and argue (by establishing connections to other problems) that data compression (i.e. sequential prediction under the log-loss) is a fundamental problem in online learning.