Optimal Continual Learning has Perfect Memory and is NP-hard

TL;DR

This paper reveals that optimal continual learning algorithms must solve NP-hard problems and require perfect memory, explaining the success of memory-based methods over regularization approaches.

Contribution

It provides a theoretical framework showing that avoiding catastrophic forgetting entails solving NP-hard problems, highlighting the necessity of perfect memory in continual learning.

Findings

Optimal CL algorithms solve NP-hard problems.

Memory-based CL methods perform better than regularization-based ones.

Perfect memory is required for optimal continual learning.

Abstract

Continual Learning (CL) algorithms incrementally learn a predictor or representation across multiple sequentially observed tasks. Designing CL algorithms that perform reliably and avoid so-called catastrophic forgetting has proven a persistent challenge. The current paper develops a theoretical approach that explains why. In particular, we derive the computational properties which CL algorithms would have to possess in order to avoid catastrophic forgetting. Our main finding is that such optimal CL algorithms generally solve an NP-hard problem and will require perfect memory to do so. The findings are of theoretical interest, but also explain the excellent performance of CL algorithms using experience replay, episodic memory and core sets relative to regularization-based approaches.