A Regularization Approach to Learning Task Relationships in Multitask Learning

Multitask learning is a learning paradigm that seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this article, we propose a regularization approach to learning the relationships between tasks in multitask learning. This approach can be viewed as a novel generalization of the regularized formulation for single-task learning. Besides modeling positive task correlation, our approach—multitask relationship learning (MTRL)—can also describe negative task correlation and identify outlier tasks based on the same underlying principle. By utilizing a matrix-variate normal distribution as a prior on the model parameters of all tasks, our MTRL method has a jointly convex objective function. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multitask learning setting and then generalize it to the asymmetric setting as well. We also discuss some variants of the regularization approach to demonstrate the use of other matrix-variate priors for learning task relationships. Moreover, to gain more insight into our model, we also study the relationships between MTRL and some existing multitask learning methods. Experiments conducted on a toy problem as well as several benchmark datasets demonstrate the effectiveness of MTRL as well as its high interpretability revealed by the task covariance matrix.