  Meta-learning leverages related source tasks to learn an initialization that
can be quickly fine-tuned to a target task with limited labeled examples.
However, many popular meta-learning algorithms, such as model-agnostic
meta-learning (MAML), only assume access to the target samples for fine-tuning.
In this work, we provide a general framework for meta-learning based on
weighting the loss of different source tasks, where the weights are allowed to
depend on the target samples. In this general setting, we provide upper bounds
on the distance of the weighted empirical risk of the source tasks and expected
target risk in terms of an integral probability metric (IPM) and Rademacher
complexity, which apply to a number of meta-learning settings including MAML
and a weighted MAML variant. We then develop a learning algorithm based on
minimizing the error bound with respect to an empirical IPM, including a
weighted MAML algorithm, $\alpha$-MAML. Finally, we demonstrate empirically on
several regression problems that our weighted meta-learning algorithm is able
to find better initializations than uniformly-weighted meta-learning
algorithms, such as MAML.
