One of the objectives of continual learning is to prevent catastrophic forgetting in learning multiple tasks sequentially, and the existing solutions have been driven by the conceptualization of the plasticity-stability dilemma. However, the convergence of continual learning for each sequential task is less studied so far. In this paper, we provide a convergence analysis of memory-based continual learning with stochastic gradient descent and empirical evidence that training current tasks causes the cumulative degradation of previous tasks. We propose an adaptive method for nonconvex continual learning (NCCL), which adjusts step sizes of both previous and current tasks with the gradients. The proposed method can achieve the same convergence rate as the SGD method when the catastrophic forgetting term which we define in the paper is suppressed at each iteration. Further, we demonstrate that the proposed algorithm improves the performance of continual learning over existing methods for several image classification tasks.

该论文介绍了对于连续学习中的收敛性分析，提出了一种适应性方法用于非凸连续学习，该方法调整先前和当前任务的梯度的步长，以达到与 SGD 方法相同的收敛速度，并且在减轻每次迭代的灾难性遗忘项的情况下，改进了连续学习在几个图像分类任务中的性能。

关于自适应方法在连续学习中的收敛性