Regret minimization for branching experts

Eyal Gofer, Nicolò Cesa-Bianchi, Claudio Gentile, Yishay Mansour

Research output: Contribution to journalConference articlepeer-review


We study regret minimization bounds in which the dependence on the number of experts is replaced by measures of the realized complexity of the expert class. The measures we consider are defined in retrospect given the realized losses. We concentrate on two interesting cases. In the first, our measure of complexity is the number of different "leading experts", namely, experts that were best at some point in time. We derive regret bounds that depend only on this measure, independent of the total number of experts. We also consider a case where all experts remain grouped in just a few clusters in terms of their realized cumulative losses. Here too, our regret bounds depend only on the number of clusters determined in retrospect, which serves as a measure of complexity. Our results are obtained as special cases of a more general analysis for a setting of branching experts, where the set of experts may grow over time according to a tree-like structure, determined by an adversary. For this setting of branching experts, we give algorithms and analysis that cover both the full information and the bandit scenarios.

Original languageEnglish
Pages (from-to)618-638
Number of pages21
JournalJournal of Machine Learning Research
StatePublished - 2013
Event26th Conference on Learning Theory, COLT 2013 - Princeton, NJ, United States
Duration: 12 Jun 201314 Jun 2013


  • Hedge Algorithm
  • Regret Minimization
  • Structured Experts


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