Our experimental contributions are multifold.

Figure 1: Results on 8 visually different tasks (left), comparison with Re-training (middle), and Atari RL (right). AlexNet and re-trains for each task with the entire training sets observed so far. We respectively disagree that our paper has only incremental contributions. In our opinion, "It is somehow Eq. (5) is a general expression that defines the proximal gradient descent. Our method can be also applied to the online continual learning setting.

We propose a novel regularization-based continual learning method, dubbed as Adaptive Group Sparsity based Continual Learning (AGS-CL), using two group sparsity-based penalties. Our method selectively employs the two penalties when learning each node based its the importance, which is adaptively updated after learning each new task. By utilizing the proximal gradient descent method for learning, the exact sparsity and freezing of the model is guaranteed, and thus, the learner can explicitly control the model capacity as the learning continues. Furthermore, as a critical detail, we re-initialize the weights associated with unimportant nodes after learning each task in order to prevent the negative transfer that causes the catastrophic forgetting and facilitate efficient learning of new tasks. Throughout the extensive experimental results, we show that our AGS-CL uses much less additional memory space for storing the regularization parameters, and it significantly outperforms several state-of-the-art baselines on representative continual learning benchmarks for both supervised and reinforcement learning tasks.