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We consider applying computer vision to video on cloud-backed mobile devices using Deep Neural Networks (DNNs). The computational demands of DNNs are high enough that, without careful resource management, such applications strain device battery, wireless data, and cloud cost budgets. We pose the corresponding resource management problem, which we call Approximate Model Scheduling, as one of serving a stream of heterogeneous (i.e., solving multiple classification problems) requests under resource constraints. We present the design and implementation of an optimizing compiler and runtime scheduler to address this problem. Going beyond traditional resource allocators, we allow each request to be served approximately, by systematically trading off DNN classification accuracy for resource use, and remotely, by reasoning about on-device/cloud execution trade-offs. To inform the resource …