Robust approachability and regret minimization in games with partial monitoring

Shie Mannor (1) , Vianney Perchet (2) , Gilles Stoltz (3, 4, 5)

1 EE-Technion - Department of Electrical Engineering - Technion [Haïfa]
2 CMLA - Centre de Mathématiques et de Leurs Applications
3 DMA - Département de Mathématiques et Applications - ENS Paris
4 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
5 CLASSIC - Computational Learning, Aggregation, Supervised Statistical, Inference, and Classification

Approachability has become a standard tool in analyzing learning algorithms in the adversarial online learning setup. We develop a variant of approachability for games where there is ambiguity in the obtained reward that belongs to a set, rather than being a single vector. Using this variant we tackle the problem of approachability in games with partial monitoring and develop simple and efficient algorithms (i.e., with constant per-step complexity) for this setup. We finally consider external and internal regret in repeated games with partial monitoring, for which we derive regret-minimizing strategies based on approachability theory.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Apprentissage [cs.LG]

Shie Mannor, Vianney Perchet, Gilles Stoltz. Robust approachability and regret minimization in games with partial monitoring. The 24rd Annual Conference on Learning Theory - COLT 2011, Jul 2011, Budapest, Hungary. pp. . ⟨hal-00595695v1⟩