Learning from ranking observations arises in many domains, and siamese deep neural networks have shown excellent inference performance in this setting. However, SGD does not scale well, as an epoch grows exponentially with the ranking observation size. We show that a spectral algorithm can be combined with deep learning methods to significantly accelerate training. We combine a spectral estimate of Plackett-Luce ranking scores with a deep model via the Alternating Directions Method of Multipliers with a Kullback-Leibler proximal penalty. Compared to a state-of-the-art siamese network, our algorithms are up to 175 times faster and attain better predictions by up to 26% Top-1 Accuracy and 6% Kendall-Tau correlation over five real-life ranking datasets.