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Dual-panel displays require local dimming algorithms in order to reproduce content with high fidelity and high dynamic range. In this work, a novel deep learning based local dimming method is proposed for rendering HDR images on dual-panel HDR displays. The method uses a Convolutional Neural Network to predict backlight values, using as input the HDR image that is to be displayed. The model is designed and trained via a controllable power parameter that allows a user to trade off between power and quality. The proposed method is evaluated against six other methods on a test set of 105 HDR images, using a variety of quantitative quality metrics. Results demonstrate improved display quality and better power consumption when using the proposed method compared to the best alternatives.