[edit]
Fixed Design Analysis of Regularization-Based Continual Learning
Proceedings of The 2nd Conference on Lifelong Learning Agents, PMLR 232:513-533, 2023.
Abstract
We consider a continual learning (CL) problem with two linear regression tasks in the fixed design setting, where the feature vectors are assumed fixed and the labels are assumed to be random variables. We consider an ℓ2-regularized CL algorithm, which computes an Ordinary Least Squares parameter to fit the first dataset, then computes another parameter that fits the second dataset under an ℓ2-regularization penalizing its deviation from the first parameter, and outputs the second parameter. For this algorithm, we provide tight upper and lower bounds on the average risk over the two tasks. Our risk bounds reveal a provable trade-off between forgetting and intransigence of the ℓ2-regularized CL algorithm: with a large regularization parameter, the algorithm output forgets less information about the first task but is intransigent to extract new information from the second task; and vice versa. Our results suggest that catastrophic forgetting could happen for CL with dissimilar tasks (under a precise similarity measurement), and that a well-tuned ℓ2-regularization can partially mitigate this issue by introducing intransigence.