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An increasing number of mobile applications rely on Machine Learning (ML) routines for analyzing data. Executing such tasks at the user devices saves the energy spent on transmitting and processing large data volumes at distant cloud-deployed servers. However, due to memory and computing limitations, the devices often cannot support the required resource-intensive routines and fail to accurately execute the tasks. In this work, we address the problem of edge-assisted analytics in resource-constrained systems by proposing and evaluating a rigorous selective offloading framework. The devices execute their tasks locally and outsource them to cloudlet servers only when they predict a significant performance improvement. We consider the practical scenario where the offloading gain and resource costs are time-varying; and propose an online optimization algorithm that maximizes the service performance without requiring to know this information. Our approach relies on an approximate dual subgradient method combined with a primal-averaging scheme, and works under minimal assumptions about the system stochasticity. We fully implement the proposed algorithm in a wireless testbed and evaluate its performance using a state-of-the-art image recognition application, finding significant performance gains and cost savings.