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