Online Multi-task Learning with Hard Constraints

Gabor Lugosi (1) , Omiros Papaspiliopoulos (1) , Gilles Stoltz (2, 3)

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

We discuss multi-task online learning when a decision maker has to deal simultaneously with M tasks. The tasks are related, which is modeled by imposing that the M-tuple of actions taken by the decision maker needs to satisfy certain constraints. We give natural examples of such restrictions and then discuss a general class of tractable constraints, for which we introduce computationally efficient ways of selecting actions, essentially by reducing to an on-line shortest path problem. We briefly discuss ``tracking'' and ``bandit'' versions of the problem and extend the model in various ways, including non-additive global losses and uncountably infinite sets of tasks.

Domaines: Machine Learning [stat.ML]; Théorie [stat.TH]; Statistiques [math.ST]; Autres [stat.ML]; Apprentissage [cs.LG]

Gabor Lugosi, Omiros Papaspiliopoulos, Gilles Stoltz. Online Multi-task Learning with Hard Constraints. 2009. ⟨hal-00362643v2⟩