How Fine-Tuning Allows for Effective Meta-Learning

TL;DR

This paper provides a theoretical analysis of how fine-tuning in meta-learning, exemplified by MAML, can effectively leverage shared representations across tasks, with risk bounds demonstrating its advantages over frozen representations.

Contribution

The paper introduces a theoretical framework for analyzing MAML-like algorithms, deriving risk bounds for fine-tuning, and comparing their effectiveness to non-fine-tuning methods.

Findings

Risk bounds show fine-tuning can leverage shared structure effectively.

Guarantees instantiated for logistic regression and neural networks.

Existence of worst-case scenarios where fine-tuning outperforms frozen representations.

Abstract

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.