A Spectral Regularization Framework for Multi-Task Structure Learning

Abstract

Learning the common structure shared by a set of supervised tasks is an important practical and theoretical problem. Knowledge of this structure may lead to better generalization performance on the tasks and may also facilitate learning new tasks. We propose a framework for solving this problem, which is based on regularization with spectral functions of matrices. This class of regularizers exhibits appealing computational properties and can be optimized efficiently by an alternating minimization algorithm. We provide a necessary and sufficient condition for convexity of the regularizer. We analyze concrete examples of the framework which are equivalent to regularization with Lp matrix norms. Experiments on two real data sets indicate that the algorithm scales well with the number of tasks and improves on state of the art statistical performance. 1