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Adaptive optimization algorithms enjoy fast convergence and have been widely exploited in pattern recognition and cognitively-inspired machine learning. These algorithms may however be of high computational cost and low generalization ability due to their projection steps. Such limitations make them difficult to be applied in big data analytics, which may typically be seen in cognitively inspired learning, e.g. deep learning tasks. In this paper, we propose a fast and accurate adaptive momentum online algorithm, called LightAdam, to alleviate the drawbacks of projection steps for the adaptive algorithms. The proposed algorithm substantially reduces computational cost for each iteration step by replacing high-order projection operators with one-dimensional linear searches. Moreover, we introduce a novel second-order momentum and engage dynamic learning rate bounds in the proposed algorithm, thereby …