Strategies for prediction under imperfect monitoring

Gabor Lugosi (1) , Shie Mannor (2) , Gilles Stoltz (3, 4)

1 ICREA - Institució Catalana de Recerca i Estudis Avançats = Catalan Institution for Research and Advanced Studies
2 McGill University = Université McGill [Montréal, Canada]
3 DMA - Département de Mathématiques et Applications - ENS Paris
4 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC

We propose simple randomized strategies for sequential prediction under imperfect monitoring, that is, when the forecaster does not have access to the past outcomes but rather to a feedback signal. The proposed strategies are consistent in the sense that they achieve, asymptotically, the best possible average reward. It was Rustichini (1999) who first proved the existence of such consistent predictors. The forecasters presented here offer the first constructive proof of consistency. Moreover, the proposed algorithms are computationally efficient. We also establish upper bounds for the rates of convergence. In the case of deterministic feedback, these rates are optimal up to logarithmic terms.

Keywords: individual sequences; repeated games with partial monitoring; approachability

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]; Machine Learning [cs.LG]

Gabor Lugosi, Shie Mannor, Gilles Stoltz. Strategies for prediction under imperfect monitoring. Mathematics of Operations Research, 2008, à paraître. ⟨hal-00124679v4⟩