Mobile crowdsourcing has long promised to utilize the power of mobile crowds to reduce the time and monetary cost required to perform large-scale location-dependent tasks, e.g., environmental sensing. Assigning the right tasks to the right users, however, is a longstanding challenge: different users will be better suited for different tasks, which in turn will have different contributions to the overall crowdsourcing goal. Even worse, these relationships are generally unknown a priori and may change over time, particularly in mobile settings. The diversity of devices in the Internet of Things and diversity of new application tasks that they may run exacerbate these challenges. Thus, in this paper, we formulate the mobile crowdsourcing problem as a Contextual Combinatorial Volatile Multi-armed Bandit problem. Although prior work has attempted to learn the optimal user-task assignment based on user-specific side information, such formulations assume known structure in the relationships between contextual information, user suitability for each task, and the overall crowdsourcing goal. To relax these assumptions, we propose a Neural-MAB algorithm that can learn these relationships. We show that in a simulated mobile crowdsourcing application, our algorithm significantly outperforms existing multi-armed bandit baselines in settings with both known and unknown reward structures.