This paper considers a setting where embedded devices are used to acquire and classify images. Because of limited computing capacity, embedded devices rely on a parsimonious classification model with uneven accuracy. When local classification is deemed inaccurate, devices can decide to offload the image to an edge server with a more accurate but resource-intensive model. Resource constraints, e.g., network bandwidth, however, require regulating such transmissions to avoid congestion and high latency. The paper investigates this offloading problem when transmissions regulation is through a token bucket, a mechanism commonly used for such purposes. The goal is to devise a lightweight, online offloading policy that optimizes an application-specific metric (e.g., classification accuracy) under the constraints of the token bucket. The paper develops a policy based on a Deep Q-Network (DQN), and demonstrates both its efficacy and the feasibility of its deployment on embedded devices. Of note is the fact that the policy can handle complex input patterns, including correlation in image arrivals and classification accuracy. The evaluation is carried out by performing image classification over a local testbed using synthetic traces generated from the ImageNet image classification benchmark. Implementation of this work is available at https://github.com/qiujiaming315/edgeml-dqn.