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Unmanned aerial systems (UAS) are increasingly used in precision agriculture to collect crop health related data. UAS can capture data more often and more cost-effectively than sending human scouts into the field. However, in large crop fields, flight time, and hence data collection, is limited by battery life. In a conventional UAS approach, human operators are required to exchange depleted batteries many times, which can be costly and time consuming. In this study, we developed a novel, fully autonomous aerial scouting approach that preserves battery life by sampling sections of a field for sensing and predicting crop health for the whole field. Our approach uses reinforcement learning (RL) and convolutional neural networks (CNN) to accurately and autonomously sample the field. To develop and test the approach, we ran flight simulations on an aerial image dataset collected from an 80-acre corn field. The excess green vegetation Index was used as a proxy for crop health condition. Compared to the conventional UAS scouting approach, the proposed scouting approach sampled 40% of the field, predicted crop health with 89.8% accuracy, reduced labor cost by 4.8× and increased agricultural profits by 1.36×.