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In lifelong learning, tasks (or classes) to be learned arrive sequentiallyover time in arbitrary order. During training, knowledge from previous taskscan be captured and transferred to subsequent ones to improve sampleefficiency. We consider the setting where all target tasks can be representedin the span of a small number of unknown linear or nonlinear features of theinput data. We propose a lifelong learning algorithm that maintains and refinesthe internal feature representation. We prove that for any desired accuracy onall tasks, the dimension of the representation remains close to that of theunderlying representation. The resulting sample complexity improvessignificantly on existing bounds. In the setting of linear features, ouralgorithm 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 lowerbound for any lifelong learning algorithm that uses a single task learner as ablack box. We complement our analysis with an empirical study, including aheuristic lifelong learning algorithm for deep neural networks. Our methodperforms favorably on challenging realistic image datasets compared tostate-of-the-art continual learning methods.

Provable Lifelong Learning of Representations