The evaluation of hyperparameters, neural architectures, or data augmentation policies becomes a critical problem in advanced deep model training with a large hyperparameter search space. In this paper, we propose an efficient and robust bandit-based algorithm called Sub-Sampling (SS) in the scenario of hyperparameter search evaluation and its modified version for high GPU usage. It evaluates the potential of hyperparameters by the sub-samples of observations and is theoretically proved to be optimal under the criterion of cumulative regret. We further combine SS with Bayesian Optimization and develop a novel hyperparameter optimization algorithm called BOSS. Empirical studies validate our theoretical arguments of SS and demonstrate the superior performance of BOSS on a number of applications, including Neural Architecture Search (NAS), Data Augmentation (DA), Object Detection (OD), and Reinforcement Learning (RL).