Provable Meta-Learning of Linear Representations

TL;DR

This paper develops provably efficient algorithms for meta-learning linear representations across multiple tasks, providing theoretical guarantees and lower bounds for sample complexity in transfer learning scenarios.

Contribution

It introduces the first provably fast algorithms for learning shared linear features in multi-task regression and establishes fundamental lower bounds on sample complexity.

Findings

Algorithms achieve sample-efficient learning of shared features

Theoretical guarantees for transfer to new tasks

Lower bounds on sample complexity are established

Abstract

Meta-learning, or learning-to-learn, seeks to design algorithms that can utilize previous experience to rapidly learn new skills or adapt to new environments. Representation learning -- a key tool for performing meta-learning -- learns a data representation that can transfer knowledge across multiple tasks, which is essential in regimes where data is scarce. Despite a recent surge of interest in the practice of meta-learning, the theoretical underpinnings of meta-learning algorithms are lacking, especially in the context of learning transferable representations. In this paper, we focus on the problem of multi-task linear regression -- in which multiple linear regression models share a common, low-dimensional linear representation. Here, we provide provably fast, sample-efficient algorithms to address the dual challenges of (1) learning a common set of features from multiple, related tasks, and (2) transferring this knowledge to new, unseen tasks. Both are central to the general problem of meta-learning. Finally, we complement these results by providing information-theoretic lower bounds on the sample complexity of learning these linear features.