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We discuss multi-task online learning when a decision maker has to dealsimultaneously with M tasks. The tasks are related, which is modeled byimposing that the M-tuple of actions taken by the decision maker needs tosatisfy certain constraints. We give natural examples of such restrictions andthen discuss a general class of tractable constraints, for which we introducecomputationally efficient ways of selecting actions, essentially by reducing toan on-line shortest path problem. We briefly discuss "tracking" and "bandit"versions of the problem and extend the model in various ways, includingnon-additive global losses and uncountably infinite sets of tasks.

Online Multi-task Learning with Hard Constraints