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Aiming at a mathematical foundation for kernel methods in coefficientregularization for multi-task learning, we investigate theory of vector-valuedreproducing kernel Banach spaces (RKBS) with L_{p,1}-norms, which contains thesparse learning scheme $p=1$ and the group lasso p=2. We construct RKBSs thatare equipped with such group lasso norms and admit the linear representertheorem for regularized learning schemes. The corresponding kernels that areadmissible for the construction are discussed.

Vector-valued Reproducing Kernel Banach Spaces with Group Lasso Norms