Online multi-task learning with hard constraints
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.