Optimal Continual Learning has Perfect Memory and is NP-hard
This work provides a theoretical explanation for the persistent difficulties in designing reliable continual learning algorithms, which is incremental as it builds on existing CL challenges.
The paper tackles the challenge of catastrophic forgetting in continual learning by deriving the computational properties needed for optimal algorithms, finding that they must solve an NP-hard problem and require perfect memory. This explains the superior performance of methods like experience replay over regularization-based approaches.
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.