Provable Lifelong Learning of Representations
This addresses the challenge of efficient knowledge transfer across sequential tasks in machine learning, with incremental theoretical and empirical improvements.
The paper tackles the problem of lifelong learning where tasks arrive sequentially, proposing an algorithm that maintains and refines feature representations to improve sample efficiency, with proven bounds showing sample complexity of $ ilde{O}(dk^{1.5}/ε+km/ε)$ for linear features and favorable empirical performance on image datasets.
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 $ε$ is $\tilde{O}(dk^{1.5}/ε+km/ε)$. 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.