  We build a theoretical framework for designing and understanding practical
meta-learning methods that integrates sophisticated formalizations of
task-similarity with the extensive literature on online convex optimization and
sequential prediction algorithms. Our approach enables the task-similarity to
be learned adaptively, provides sharper transfer-risk bounds in the setting of
statistical learning-to-learn, and leads to straightforward derivations of
average-case regret bounds for efficient algorithms in settings where the
task-environment changes dynamically or the tasks share a certain geometric
structure. We use our theory to modify several popular meta-learning algorithms
and improve their meta-test-time performance on standard problems in few-shot
learning and federated learning.
