The quality of machine learning (ML) and deep learning (DL) models are very sensitive to many different adjustable parameters that are set before training even begins, commonly called hyperparameters. Efficient hyperparameter exploration is of great importance to practitioners in order to find high-quality models with affordable time and cost. This is however a challenging process due to a huge search space, expensive training runtime, sparsity of good configurations, and scarcity of time and resources. We develop a scheduling algorithm POP that quickly identifies among promising, opportunistic and poor configurations of hyperparameters. It infuses probabilistic model-based classification with dynamic scheduling and early termination to jointly optimize quality and cost. We also build a comprehensive hyperparameter exploration infrastructure, HyperDrive, to support existing and future scheduling algorithms for a wide range of usage scenarios across different ML/DL frameworks and learning domains. We evaluate POP and HyperDrive using complex and deep models. The results show that we speed up the training process by up to 6.7x compared with basic approaches like random/grid search and up to 2.1x compared with state-of-the-art approaches while achieving similar model quality compared with prior work.