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.