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We present the first optimal rates for infinite-dimensional vector-valuedridge regression on a continuous scale of norms that interpolate between $L_2$and the hypothesis space, which we consider as a vector-valued reproducingkernel Hilbert space. These rates allow to treat the misspecified case in whichthe true regression function is not contained in the hypothesis space. Wecombine standard assumptions on the capacity of the hypothesis space with anovel tensor product construction of vector-valued interpolation spaces inorder to characterize the smoothness of the regression function. Our upperbound not only attains the same rate as real-valued kernel ridge regression,but also removes the assumption that the target regression function is bounded.For the lower bound, we reduce the problem to the scalar setting using aprojection argument. We show that these rates are optimal in most cases andindependent of the dimension of the output space. We illustrate our results forthe special case of vector-valued Sobolev spaces.

Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithm