Aggregating Algorithm for prediction of packs

Abstract

This paper formulates a protocol for prediction of packs, which is a special case of on-line prediction under delayed feedback. Under the prediction of packs protocol, the learner must make a few predictions without seeing the respective outcomes and then the outcomes are revealed in one go. The paper develops the theory of prediction with expert advice for packs by generalising the concept of mixability. We propose a number of merging algorithms for prediction of packs with tight worst case loss upper bounds similar to those for Vovk’s Aggregating Algorithm. Unlike existing algorithms for delayed feedback settings, our algorithms do not depend on the order of outcomes in a pack. Empirical experiments on sports and house price datasets are carried out to study the performance of the new algorithms and compare them against an existing method.