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Deep Neural Networks (DNNs) have shown significant advantages in a wide variety of domains. However, DNNs are becoming computationally intensive and energy hungry at an exponential pace, while at the same time, there is a vast demand for running sophisticated DNN-based services on resource constrained embedded devices. In this paper, we target energy-efficient inference on embedded DNN accelerators. To that end, we propose an automated framework to compress DNNs in a hardware-aware manner by jointly employing pruning and quantization. We explore, for the first time, per-layer fine- and coarse-grained pruning, in the same DNN architecture, in addition to low bit-width mixed-precision quantization for weights and activations. Reinforcement Learning (RL) is used to explore the associated design space and identify the pruning-quantization configuration so that the energy consumption is minimized whilst the prediction accuracy loss is retained at acceptable levels. Using our novel composite RL agent we are able to extract energy-efficient solutions without requiring retraining and/or fine-tuning. Our extensive experimental evaluation over widely used DNNs and the CIFAR-10/100 and ImageNet datasets demonstrates that our framework achieves 39% average energy reduction for 1.7% average accuracy loss and outperforms significantly the state-of-the-art approaches.