  Representation learning has been widely studied in the context of
meta-learning, enabling rapid learning of new tasks through shared
representations. Recent works such as MAML have explored using
fine-tuning-based metrics, which measure the ease by which fine-tuning can
achieve good performance, as proxies for obtaining representations. We present
a theoretical framework for analyzing representations derived from a MAML-like
algorithm, assuming the available tasks use approximately the same underlying
representation. We then provide risk bounds on the best predictor found by
fine-tuning via gradient descent, demonstrating that the algorithm can provably
leverage the shared structure. The upper bound applies to general function
classes, which we demonstrate by instantiating the guarantees of our framework
in the logistic regression and neural network settings. In contrast, we
establish the existence of settings where any algorithm, using a representation
trained with no consideration for task-specific fine-tuning, performs as well
as a learner with no access to source tasks in the worst case. This separation
result underscores the benefit of fine-tuning-based methods, such as MAML, over
methods with "frozen representation" objectives in few-shot learning.
