Title: Nonconvex Continual Learning with Episodic Memory. Abstract: Continual learning aims to prevent catastrophic forgetting while learning a new task without accessing data of previously learned tasks. 
The memory for such learning scenarios build a small subset of the data for previous tasks and is used in various ways such as quadratic programming and sample selection. 
Current memory-based continual learning algorithms are formulated as a constrained optimization problem and rephrase constraints as a gradient-based approach.
However, previous works have not provided the theoretical proof on convergence to previously learned tasks.
In this paper, we propose a theoretical convergence analysis of continual learning based on stochastic gradient descent method.
Our method, nonconvex continual learning (NCCL), can achieve the same convergence rate when the proposed catastrophic forgetting term is suppressed at each iteration.
We also show that memory-based approaches have an inherent problem of overfitting to memory, which degrades the performance on previously learned tasks, namely catastrophic forgetting.
We empirically demonstrate that NCCL successfully performs continual learning with episodic memory by scaling learning rates adaptive to mini-batches on several image classification tasks.  