Data-dependent and Oracle Bounds on Forgetting in Continual Learning
This work addresses the theoretical gap in continual learning by providing general bounds on forgetting, which is a critical issue for practitioners developing robust AI systems, though it is incremental as it builds on existing theoretical frameworks.
The paper tackles the problem of quantifying and bounding forgetting in continual learning for exemplar-free methods, providing both data-dependent and oracle bounds that apply regardless of model and algorithm choice, and demonstrates empirically that their approach yields tight and practical bounds on forgetting for several problems and algorithms.
In continual learning, knowledge must be preserved and re-used between tasks, maintaining good transfer to future tasks and minimizing forgetting of previously learned ones. While several practical algorithms have been devised for this setting, there have been few theoretical works aiming to quantify and bound the degree of Forgetting in general settings. For \emph{exemplar-free} methods, we provide both data-dependent upper bounds that apply \emph{regardless of model and algorithm choice}, and oracle bounds for Gibbs posteriors. We derive an algorithm based on our bounds and demonstrate empirically that our approach yields tight and practical bounds on forgetting for several continual learning problems and algorithms.