Convex Multi-Task Learning by Clustering

We consider the problem of multi-task learning in which tasks belong to hidden clusters. We formulate the learning problem as a novel convex optimization problem in which linear classifiers are combinations of (a small number of) some basis. Our formulation jointly learns both the basis and the linear combination. We propose a scalable optimization algorithm for finding the optimal solution. Our new methods outperform existing state-of-the-art methods on multi-task sentiment classification tasks.