  Reducing the amount of human supervision is a key problem in machine learning
and a natural approach is that of exploiting the relations (structure) among
different tasks. This is the idea at the core of multi-task learning. In this
context a fundamental question is how to incorporate the tasks structure in the
learning problem.We tackle this question by studying a general computational
framework that allows to encode a-priori knowledge of the tasks structure in
the form of a convex penalty; in this setting a variety of previously proposed
methods can be recovered as special cases, including linear and non-linear
approaches. Within this framework, we show that tasks and their structure can
be efficiently learned considering a convex optimization problem that can be
approached by means of block coordinate methods such as alternating
minimization and for which we prove convergence to the global minimum.
