Shared spectrum systems facilitate spectrum allocation to unlicensed users without harming the licensed users; they offer great promise in optimizing spectrum utility, but their management (in particular, efficient spectrum allocation to unlicensed users) is challenging. A significant shortcoming of current allocation methods is that they are either done very conservatively to ensure correctness, or are based on imperfect propagation models and/or spectrum sensing with poor spatial granularity. This leads to poor spectrum utilization, the fundamental objective of shared spectrum systems. To allocate spectrum near-optimally to secondary users in general scenarios, we fundamentally need to have knowledge of the signal path-loss function. In practice, however, even the best known path-loss models have unsatisfactory accuracy, and conducting extensive surveys to gather path-loss values is infeasible. To circumvent this challenge, we propose to learn the spectrum allocation function directly using supervised learning techniques. We particularly address the scenarios when the primary users' information may not be available; for such settings, we make use of a crowdsourced sensing architecture and use the spectrum sensor readings as features. We develop an efficient CNN-based approach (called DeepAlloc) and address various challenges that arise in its application to the learning the spectrum allocation function. Via extensive large-scale simulation and a small testbed, we demonstrate the effectiveness of our developed techniques; in particular, we observe that our approach improves the accuracy of standard learning techniques and prior work by up to 60%.