Aggregating Algorithm for prediction of packs

Dmitry Adamskiy, Anthony Bellotti, Raisa Dzhamtyrova, Yuri Kalnishkan

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)1231-1260
Number of pages30
JournalMachine Learning
Issue number8-9
Early online date7 Jan 2019
Publication statusPublished - 15 Sept 2019


  • on-line learning
  • prediction with expert advice
  • Sport
  • House price

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