Online Learning and Game Theory. A Quick Overview with recent results and applications^*

¹ Aix-Marseille University, CNRS and EHESS, Centre de la vieille Charité, 2 rue de la Charité, 13002 Marseille, France
² EDF R&D, Clamart, France & GREGHEC (HEC Paris, CNRS), Jouy-en-Josas, France
³ INRIA Grenoble Rhône-Alpes, LIG laboratoire d’Informatique de Grenoble, MESCAL
⁴ Laboratoire de Probabiliés et Modèles Aléatoires, Université Paris Diderot, Paris, France & Equipe Sierra, INRIA - ENS Paris, Paris, France

Abstract

We study one of the main concept of online learning and sequential decision problem known as regret minimization. We investigate three different frameworks, whether data are generated accordingly to some i.i.d. process, or when no assumption whatsoever are made on their generation and, finally, when they are the consequences of some sequential interactions between players.

The overall objective is to provide a comprehensive introduction to this domain. In each of these main setups, we define and analyze classical algorithms and we analyze their performances. Finally, we also show that some concepts of equilibria that emerged in game theory are learnable by players using online learning schemes while some other concepts are not learnable.