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Though neural networks have achieved much progress in various applications,it is still highly challenging for them to learn from a continuous stream oftasks without forgetting. Continual learning, a new learning paradigm, aims tosolve this issue. In this work, we propose a new model for continual learning,called Bayesian Optimized Continual Learning with Attention Mechanism (BOCL)that dynamically expands the network capacity upon the arrival of new tasks byBayesian optimization and selectively utilizes previous knowledge (e.g. featuremaps of previous tasks) via attention mechanism. Our experiments on variants ofMNIST and CIFAR-100 demonstrate that our methods outperform thestate-of-the-art in preventing catastrophic forgetting and fitting new tasksbetter.