Abstract Deep Neural Networks (DNNs) are typically trained by backpropagation in a batch setting, requiring the entire training data to be made available prior to the learning task. This is not scalable for many real-world scenarios where new data arrives sequentially in a stream. We aim to address an open challenge of “Online Deep Learning” (ODL) for learning DNNs on the fly in an online setting. Unlike traditional online learning that often optimizes some convex objective function with respect to a shallow model (e.g., a linear/kernel-based hypothesis), ODL is more challenging as the optimization objective is non-convex, and regular DNN with standard backpropagation does not work well in practice for online settings. We present a new ODL framework that attempts to tackle the challenges by learning DNN models which dynamically adapt depth from a sequence of training data in an online learning setting. Specifically, we propose a novel Hedge Backpropagation (HBP) method for online updating the parameters of DNN effectively, and validate the efficacy on large data sets (both stationary and concept drifting scenarios).