In this paper, we propose an Active Learning (AL) framework for the Multi-Task Adaptive Filtering (MTAF) problem. Specifically, we explore AL approaches to rapidly improve an MTAF system, based on Dirichlet Process priors, with minimal user/task-level feedback. The proposed AL approaches select instances for delivery with a two-fold objective: 1) Improve future task-specific system performance based on feedback received on delivered instances for that task, 2) Improve the future overall system performance, thereby benefiting other tasks in the system, based on feedback received on delivered instances for a particular task. Current AL approaches focus only on the first objective. For satisfying both goals, we define a new scoring function called Utility Gain to estimate the perceived improvements in task-specific and global models. In our experiments on standard benchmark datasets, we observed that global AL approaches that additionally take into account the potential benefit of feedba...