This paper presents two novel formulations for learning shared feature representations across multiple tasks. The idea is to pose the problem as that of learning a shared kernel, which is constructed from a given set of base kernels, leading to improved generalization in all the tasks. The first formulation employs a (l1,lp), p ≥ 2 mixed norm regularizer promoting sparse combinations of the base kernels and unequal weightings across tasks - enabling the formulation to work with unequally reliable tasks. While this convex formulation can be solved using a suitable mirror-descent algorithm, it may not learn shared feature representations which are sparse. The second formulation extends these ideas for learning sparse feature representations constructed from multiple base kernels and shared across multiple tasks. The sparse feature representation learnt by this formulation is essentially a direct product of low-dimensional subspaces lying in the induced feature spaces of few base kernels. The formulation is posed as a (l 1,lq),q ≥ 1 mixed Schattennorm regularized problem. One main contribution of this paper is a novel mirror-descent based algorithm for solving this problem which is not a standard set-up studied in the optimization literature. The proposed formulations can also be understood as generalizations of the framework of multiple kernel learning to the case of multiple tasks and hence are suitable for various learning applications. Simulation results on real-world datasets show that the proposed formulations generalize better than state-of-the-art. The results also illustrate the efficacy of the proposed mirror-descent based algorithms. Copyright © SIAM.