  Meta learning aims at learning a model that can quickly adapt to unseen
tasks. Widely used meta learning methods include model agnostic meta learning
(MAML), implicit MAML, Bayesian MAML. Thanks to its ability of modeling
uncertainty, Bayesian MAML often has advantageous empirical performance.
However, the theoretical understanding of Bayesian MAML is still limited,
especially on questions such as if and when Bayesian MAML has provably better
performance than MAML. In this paper, we aim to provide theoretical
justifications for Bayesian MAML's advantageous performance by comparing the
meta test risks of MAML and Bayesian MAML. In the meta linear regression, under
both the distribution agnostic and linear centroid cases, we have established
that Bayesian MAML indeed has provably lower meta test risks than MAML. We
verify our theoretical results through experiments.
