Blackwell Approachability and no-regret learning are equivalent

Jacob Abernethy, Peter L. Bartlett, Elad Hazan

Research output: Contribution to journalConference articlepeer-review

49 Scopus citations


We consider the celebrated Blackwell Approachability Theorem for two-player games with vector payoffs. Blackwell himself previously showed that the theorem implies the existence of a "no-regret" algorithm for a simple online learning problem. We show that this relationship is in fact much stronger, that Blackwell's result is equivalent to, in a very strong sense, the problem of regret minimization for Online Linear Optimization. We show that any algorithm for one such problem can be efficiently converted into an algorithm for the other. We provide one novel application of this reduction: the first efficient algorithm for calibrated forecasting.

Original languageEnglish (US)
Pages (from-to)27-46
Number of pages20
JournalJournal of Machine Learning Research
StatePublished - 2011
Externally publishedYes
Event24th International Conference on Learning Theory, COLT 2011 - Budapest, Hungary
Duration: Jul 9 2011Jul 11 2011

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


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