Adaptive Online Prediction by Following the Perturbed Leader

When applying aggregating strategies to Prediction with Expert Advice, the learning rate must be adaptively tuned. The natural choice of √ complexity/current loss renders the analysis of Weighted Majority derivatives quite complicated. In particular, for arbitrary weights there have been no results proven so far. The analysis of the alternative “Follow the Perturbed Leader” (FPL) algorithm from Kalai and Vempala (2003) based on Hannan’s algorithm is easier. We derive loss bounds for adaptive learning rate and both finite expert classes with uniform weights and countable expert classes with arbitrary weights. For the former setup, our loss bounds match the best known results so far, while for the latter our results are new.