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Accurate identification of important objects in the scene is a prerequisite for safe and high-quality decision making and motion planning of intelligent agents (e.g., autonomous vehicles) that navigate in complex and dynamic environments. Most existing approaches attempt to employ attention mechanisms to learn importance weights associated with each object indirectly via various tasks (e.g., trajectory prediction), which do not enforce direct supervision on the importance estimation. In contrast, we tackle this task in an explicit way and formulate it as a binary classification ("important" or "unimportant") problem. We propose a novel approach for important object identification in egocentric driving scenarios with relational reasoning on the objects in the scene. Besides, since human annotations are limited and expensive to obtain, we present a semi-supervised learning pipeline to enable the model to learn from unlimited unlabeled data. Moreover, we propose to leverage the auxiliary tasks of ego vehicle behavior prediction to further improve the accuracy of importance estimation. The proposed approach is evaluated on a public egocentric driving dataset (H3D) collected in complex traffic scenarios. A detailed ablative study is conducted to demonstrate the effectiveness of each model component and the training strategy. Our approach also outperforms rule-based baselines by a large margin.