Meta-Learning and Universality: Deep Representations and Gradient Descent can Approximate any Learning Algorithm

TL;DR

This paper demonstrates that deep representations combined with gradient descent can universally approximate any learning algorithm, and shows that gradient-based meta-learning generalizes better than recurrent models.

Contribution

It formalizes the universality of deep representations with gradient descent in meta-learning and compares their expressive power to recurrent models.

Findings

Deep representations with gradient descent can approximate any learning algorithm.

Gradient-based meta-learning generalizes more widely than recurrent models.

Experiments confirm the theoretical universality and superior generalization of gradient-based approaches.

Abstract

Learning to learn is a powerful paradigm for enabling models to learn from data more effectively and efficiently. A popular approach to meta-learning is to train a recurrent model to read in a training dataset as input and output the parameters of a learned model, or output predictions for new test inputs. Alternatively, a more recent approach to meta-learning aims to acquire deep representations that can be effectively fine-tuned, via standard gradient descent, to new tasks. In this paper, we consider the meta-learning problem from the perspective of universality, formalizing the notion of learning algorithm approximation and comparing the expressive power of the aforementioned recurrent models to the more recent approaches that embed gradient descent into the meta-learner. In particular, we seek to answer the following question: does deep representation combined with standard gradient descent have sufficient capacity to approximate any learning algorithm? We find that this is indeed true, and further find, in our experiments, that gradient-based meta-learning consistently leads to learning strategies that generalize more widely compared to those represented by recurrent models.