The rate of the update for each task is defined by a K × K interaction matrix A, which, intuitively, encodes relatedness between the tasks.
when a learner makes a mistake, the compound weight vector update rule applied is where ⊗ is the Kronecker product and I m is the identity matrix of size m. This update can be rewritten as separate updates for each task: This learning algorithm directly corresponds to the minimization of the following objective: where is the hinge loss on the example at time t. this setup can be naturally extended to other loss function and to non-linear models.