Notes for Lecture 5 : Scribe : Anupam

The experts framework consists of n experts who each make predictions every day, and an online algorithm that makes a decision after seeing all the expert predictions. At the end of the day the loss/gain for each expert is revealed. The goal of the online algorithm is to perform not much worse than the single best expert over a long period of time. We analyzed the algorithm where the initial weights of all experts is 1, the online algorithm follows expert i with probability proportional to the weight wi, and the weights are updated as wi(t+ 1) = wi(t)(1− )` (t) i . The expected loss L for this online algorithm is bounded in terms of the loss L∗ for the best expert,