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Active learning, which effectively collects informative unlabeled data for annotation, reduces the demand for labeled data. In this work, we propose to retrieve unlabeled samples with a local sensitivity and hardness-aware acquisition function. The proposed method generates data copies through local perturbations and selects data points whose predictive likelihoods diverge the most from their copies. We further empower our acquisition function by injecting the select-worst case perturbation. Our method achieves consistent gains over the commonly used active learning strategies in various classification tasks. Furthermore, we observe consistent improvements over the baselines on the study of prompt selection in prompt-based few-shot learning. These experiments demonstrate that our acquisition guided by local sensitivity and hardness can be effective and beneficial for many NLP tasks.