Online learning with feedback graphs: Beyond bandits

Noga Alon, Nicolò Cesa-Bianchi, Ofer Dekel, Tomer Koren

Research output: Contribution to journalConference articlepeer-review

62 Scopus citations


We study a general class of online learning problems where the feedback is specified by a graph. This class includes online prediction with expert advice and the multi-armed bandit problem, but also several learning problems where the online player does not necessarily observe his own loss. We analyze how the structure of the feedback graph controls the inherent difficulty of the induced T-round learning problem. Specifically, we show that any feedback graph belongs to one of three classes: strongly observable graphs, weakly observable graphs, and unobservable graphs. We prove that the first class induces learning problems with θ1/2T1/2) minimax regret, where α is the independence number of the underlying graph; the second class induces problems with θ1/3T2/3) minimax regret, where δ is the domination number of a certain portion of the graph; and the third class induces problems with linear minimax regret. Our results subsume much of the previous work on learning with feedback graphs and reveal new connections to partial monitoring games. We also show how the regret is affected if the graphs are allowed to vary with time.

Original languageEnglish (US)
JournalJournal of Machine Learning Research
Issue number2015
StatePublished - 2015
Externally publishedYes
Event28th Conference on Learning Theory, COLT 2015 - Paris, France
Duration: Jul 2 2015Jul 6 2015

All Science Journal Classification (ASJC) codes

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


Dive into the research topics of 'Online learning with feedback graphs: Beyond bandits'. Together they form a unique fingerprint.

Cite this