Adaptive Online Prediction by Following the Perturbed Leader

TL;DR

This paper develops adaptive learning rate strategies for the Follow the Perturbed Leader algorithm in online prediction, providing new theoretical loss bounds for both finite and countable expert classes with arbitrary weights.

Contribution

It introduces new loss bounds for FPL with adaptive learning rates, applicable to countable expert classes with arbitrary weights, extending prior finite expert results.

Findings

Loss bounds match best known results for finite experts.

New loss bounds established for countable expert classes with arbitrary weights.

Analysis simplifies the understanding of adaptive FPL algorithms.

Abstract

When applying aggregating strategies to Prediction with Expert Advice, the learning rate must be adaptively tuned. The natural choice of sqrt(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 & 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.