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The advances in deep neural networks (DNN) have significantly enhanced real-time detection of anomalous data in IoT applications. However, the complexity-accuracy-delay dilemma persists: Complex DNN models offer higher accuracy, but typical IoT devices can barely afford the computation load, and the remedy of offloading the load to the cloud incurs long delay. In this article, we address this challenge by proposing an adaptive anomaly detection scheme with hierarchical edge computing (HEC). Specifically, we first construct multiple anomaly detection DNN models with increasing complexity and associate each of them to a corresponding HEC layer. Then, we design an adaptive model selection scheme that is formulated as a contextual-bandit problem and solved by using a reinforcement learning policy network . We also incorporate a parallelism policy training method to accelerate the training process by taking advantage of distributed models. We build an HEC testbed using real IoT devices and implement and evaluate our contextual-bandit approach with both univariate and multivariate IoT datasets. In comparison with both baseline and state-of-the-art schemes, our adaptive approach strikes the best accuracy-delay tradeoff on the univariate dataset and achieves the best accuracy and F1-score on the multivariate dataset with only negligibly longer delay than the best (but inflexible) scheme.