  We introduce a new and rigorously-formulated PAC-Bayes meta-learning
algorithm that solves few-shot learning. Our proposed method extends the
PAC-Bayes framework from a single task setting to the meta-learning multiple
task setting to upper-bound the error evaluated on any, even unseen, tasks and
samples. We also propose a generative-based approach to estimate the posterior
of task-specific model parameters more expressively compared to the usual
assumption based on a multivariate normal distribution with a diagonal
covariance matrix. We show that the models trained with our proposed
meta-learning algorithm are well calibrated and accurate, with state-of-the-art
calibration and classification results on few-shot classification
(mini-ImageNet and tiered-ImageNet) and regression (multi-modal
task-distribution regression) benchmarks.
