Exploiting Unrelated Tasks in Multi-Task Learning

We study the problem of learning a group of principal tasks using a group of auxiliary tasks, unrelated to the principal ones. In many applications, joint learning of unrelated tasks which use the same input data can be beneficial. The reason is that prior knowledge about which tasks are unrelated can lead to sparser and more informative representations for each task, essentially screening out idiosyncrasies of the data distribution. We propose a novel method which builds on a prior multitask methodology by favoring a shared low dimensional representation within each group of tasks. In addition, we impose a penalty on tasks from different groups which encourages the two representations to be orthogonal. We further discuss a condition which ensures convexity of the optimization problem and argue that it can be solved by alternating minimization. We present experiments on synthetic and real data, which indicate that incorporating unrelated tasks can improve significantly over standard multi-task learning methods.