Provable Lifelong Learning of Representations

TL;DR

This paper introduces a provable lifelong learning algorithm that maintains a compact feature representation, improving sample efficiency and demonstrating strong empirical performance on image datasets.

Contribution

It proposes a new lifelong learning method with theoretical guarantees on representation size and sample complexity, applicable to linear and nonlinear features.

Findings

Sample complexity is significantly reduced compared to existing bounds.

The algorithm is provably efficient for linear features with near-optimal bounds.

Empirical results show competitive performance on realistic image datasets.

Abstract

In lifelong learning, tasks (or classes) to be learned arrive sequentially over time in arbitrary order. During training, knowledge from previous tasks can be captured and transferred to subsequent ones to improve sample efficiency. We consider the setting where all target tasks can be represented in the span of a small number of unknown linear or nonlinear features of the input data. We propose a lifelong learning algorithm that maintains and refines the internal feature representation. We prove that for any desired accuracy on all tasks, the dimension of the representation remains close to that of the underlying representation. The resulting sample complexity improves significantly on existing bounds. In the setting of linear features, our algorithm is provably efficient and the sample complexity for input dimension $d$, $m$ tasks with $k$ features up to error $\epsilon$ is $\tilde{O}(dk^{1.5}/\epsilon+km/\epsilon)$. We also prove a matching lower bound for any lifelong learning algorithm that uses a single task learner as a black box. We complement our analysis with an empirical study, including a heuristic lifelong learning algorithm for deep neural networks. Our method performs favorably on challenging realistic image datasets compared to state-of-the-art continual learning methods.