  In multi-task learning, a learner is given a collection of prediction tasks
and needs to solve all of them. In contrast to previous work, which required
that annotated training data is available for all tasks, we consider a new
setting, in which for some tasks, potentially most of them, only unlabeled
training data is provided. Consequently, to solve all tasks, information must
be transferred between tasks with labels and tasks without labels. Focusing on
an instance-based transfer method we analyze two variants of this setting: when
the set of labeled tasks is fixed, and when it can be actively selected by the
learner. We state and prove a generalization bound that covers both scenarios
and derive from it an algorithm for making the choice of labeled tasks (in the
active case) and for transferring information between the tasks in a principled
way. We also illustrate the effectiveness of the algorithm by experiments on
synthetic and real data.
