Memory Bounds for Continual Learning
This addresses the challenge of efficient lifelong learning for AI systems, but it is incremental as it builds on complexity theory and PAC framework.
The paper tackles the problem of continual learning by establishing memory requirements for learning sequences of tasks, showing that any continual learner needs memory linear in the number of tasks, but provides an algorithm with scalable memory when multiple passes are allowed.
Continual learning, or lifelong learning, is a formidable current challenge to machine learning. It requires the learner to solve a sequence of $k$ different learning tasks, one after the other, while retaining its aptitude for earlier tasks; the continual learner should scale better than the obvious solution of developing and maintaining a separate learner for each of the $k$ tasks. We embark on a complexity-theoretic study of continual learning in the PAC framework. We make novel uses of communication complexity to establish that any continual learner, even an improper one, needs memory that grows linearly with $k$, strongly suggesting that the problem is intractable. When logarithmically many passes over the learning tasks are allowed, we provide an algorithm based on multiplicative weights update whose memory requirement scales well; we also establish that improper learning is necessary for such performance. We conjecture that these results may lead to new promising approaches to continual learning.