# Convex Learning of Multiple Tasks and their Structure

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Carlo Ciliberto,
Youssef Mroueh,
Tomaso Poggio,
Lorenzo Rosasco
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Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1548-1557, 2015.

#### Abstract

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.

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