  Model Agnostic Meta-Learning (MAML) has emerged as a standard framework for
meta-learning, where a meta-model is learned with the ability of fast adapting
to new tasks. However, as a double-looped optimization problem, MAML needs to
differentiate through the whole inner-loop optimization path for every
outer-loop training step, which may lead to both computational inefficiency and
sub-optimal solutions. In this paper, we generalize MAML to allow meta-learning
to be defined in function spaces, and propose the first meta-learning paradigm
in the Reproducing Kernel Hilbert Space (RKHS) induced by the meta-model's
Neural Tangent Kernel (NTK). Within this paradigm, we introduce two
meta-learning algorithms in the RKHS, which no longer need a sub-optimal
iterative inner-loop adaptation as in the MAML framework. We achieve this goal
by 1) replacing the adaptation with a fast-adaptive regularizer in the RKHS;
and 2) solving the adaptation analytically based on the NTK theory. Extensive
experimental studies demonstrate advantages of our paradigm in both efficiency
and quality of solutions compared to related meta-learning algorithms. Another
interesting feature of our proposed methods is that they are demonstrated to be
more robust to adversarial attacks and out-of-distribution adaptation than
popular baselines, as demonstrated in our experiments.
