Approachability, fast and slow

Shie Mannor, Vianney Perchet

Research output: Contribution to journalConference articlepeer-review

Abstract

Approachability has become a central tool in the analysis of repeated games and online learning. A player plays a repeated vector-valued game against Nature and her objective is to have her long-term average reward inside some target set. The celebrated results of Blackwell provide a 1/√n convergence rate of the expected point-to-set distance if this is achievable, i.e., if the set is approachable. In this paper we provide a characterization for the convergence rates of approachability and show that in some cases a set can be approached with a 1/n rate. Our characterization is solely based on a combination of geometric properties of the set with properties of the repeated game, and not on additional restrictive assumptions on Nature's behavior.

Original languageEnglish
Pages (from-to)474-477
Number of pages4
JournalJournal of Machine Learning Research
Volume30
StatePublished - 2013
Event26th Conference on Learning Theory, COLT 2013 - Princeton, NJ, United States
Duration: 12 Jun 201314 Jun 2013

All Science Journal Classification (ASJC) codes

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

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