Approachability, Regret and Calibration; implications and equivalences.

Abstract : Blackwell approachability, regret minimization and calibration are three criteria evaluating a strategy (or an algorithm) in different sequential decision problems, or repeated games between a player and Nature. Although they have at first sight nothing in common, links between have been discovered: both consistent and calibrated strategies can be constructed by following, in some auxiliary game, an approachability strategy. We gathered famous or recent results and provide new ones in order to develop and generalize Blackwell's elegant theory. The final goal is to show how it can be used as a basic powerful tool to exhibit a new class of intuitive algorithms, based on simple geometric properties. In order to be complete, we also prove that approachability can be seen as a byproduct of the very existence of consistent or calibrated strategies.
Type de document :
Pré-publication, Document de travail
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Contributeur : Vianney Perchet <>
Soumis le : samedi 12 janvier 2013 - 01:20:47
Dernière modification le : mardi 11 octobre 2016 - 14:10:37
Document(s) archivé(s) le : samedi 13 avril 2013 - 02:45:09


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  • HAL Id : hal-00773218, version 1
  • ARXIV : 1301.2663



Vianney Perchet. Approachability, Regret and Calibration; implications and equivalences.. 2013. <hal-00773218>



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