Learning the Graph of Relations Among Multiple Tasks

We propose multitask Laplacian learning, a new method for jointly learning clusters of closely related tasks. Unlike standard multitask methodologies, the graph of relations among the tasks is not assumed to be known a priori, but is learned by the multitask Laplacian algorithm. The algorithm builds on kernel based methods and exploits an optimization approach for learning a continuously parameterized kernel. It involves solving a semidefinite program of a particular type, for which we develop an algorithm based on Douglas-Rachford splitting methods. Multitask Laplacian learning can find application in many cases in which tasks are related with each other to varying degrees, some strongly, others weakly. Our experiments highlight such cases in which multitask Laplacian learning outperforms independent learning of tasks and state of the art multitask learning methods. In addition, they demonstrate that our algorithm partitions the tasks into clusters each of which contains well correlated tasks.