In this paper, we present a novel approach for designing local image descriptors that learn from data and from hand-crafted descriptors. In particular, we construct a learning model that first mimics the behaviour of a hand-crafted descriptor and then learns to improve upon it in an unsupervised manner. We demonstrate the use of this knowledge-transfer framework by constructing the learned BRIEF descriptor based on the well-known hand-crafted descriptor BRIEF. We implement our learned BRIEF with a convolutional autoencoder architecture. Evaluation on the HPatches benchmark for local image descriptors shows the effectiveness of the proposed approach in the tasks of patch retrieval, patch verification, and image matching.