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The choice of learning rate (LR) functions and policies has evolved from a simple fixed LR to the decaying LR and the cyclic LR, aiming to improve the accuracy and reduce the training time of Deep Neural Networks (DNNs). This article presents a systematic approach to selecting and composing an LR policy for effective DNN training to meet desired target accuracy and reduce training time within the pre-defined training iterations. It makes three original contributions. First, we develop an LR tuning mechanism for auto-verification of a given LR policy with respect to the desired accuracy goal under the pre-defined training time constraint. Second, we develop an LR policy recommendation system (LRBench) to select and compose good LR policies from the same and/or different LR functions through dynamic tuning, and avoid bad choices, for a given learning task, DNN model, and dataset. Third, we extend LRBench by supporting different DNN optimizers and show the significant mutual impact of different LR policies and different optimizers. Evaluated using popular benchmark datasets and different DNN models (LeNet, CNN3, ResNet), we show that our approach can effectively deliver high DNN test accuracy, outperform the existing recommended default LR policies, and reduce the DNN training time by 1.6-6.7× to meet a targeted model accuracy.