MOTIVATION: With the recent advances in protein 3D structure prediction, protein interactions are becoming more central than ever before. Here, we address the problem of determining how proteins interact with one another. More specifically, we investigate the possibility of discriminating near-native protein complex conformations from incorrect ones by exploiting local environments around interfacial residues. RESULTS: Deep Local Analysis (DLA)-Ranker is a deep learning framework applying 3D convolutions to a set of locally oriented cubes representing the protein interface. It explicitly considers the local geometry of the interfacial residues along with their neighboring atoms and the regions of the interface with different solvent accessibility. We assessed its performance on three docking benchmarks made of half a million acceptable and incorrect conformations. We show that DLA-Ranker successfully identifies near-native conformations from ensembles generated by molecular docking. It surpasses or competes with other deep learning-based scoring functions. We also showcase its usefulness to discover alternative interfaces. AVAILABILITY AND IMPLEMENTATION: http://gitlab.lcqb.upmc.fr/dla-ranker/DLA-Ranker.git. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.