The light stage has been widely used in computer graphics for the past two decades, primarily to enable the relighting of human faces. By capturing the appearance of the human subject under different light sources, one obtains the light transport matrix of that subject, which enables image-based relighting in novel environments. However, due to the finite number of lights in the stage, the light transport matrix only represents a sparse sampling on the entire sphere. As a consequence, relighting the subject with a point light or a directional source that does not coincide exactly with one of the lights in the stage requires interpolation and resampling the images corresponding to nearby lights, and this leads to ghosting shadows, aliased specularities, and other artifacts. To ameliorate these artifacts and produce better results under arbitrary high-frequency lighting, this paper proposes a learning-based solution for the super-resolution of scans of human faces taken from a light stage. Given an arbitrary query light direction, our method aggregates the captured images corresponding to neighboring lights in the stage, and uses a neural network to synthesize a rendering of the face that appears to be illuminated by a virtual light source at the query location. This neural network must circumvent the inherent aliasing and regularity of the light stage data that was used for training, which we accomplish through the use of regularized traditional interpolation methods within our network. Our learned model is able to produce renderings for arbitrary light directions that exhibit realistic shadows and specular highlights, and is able to generalize across a wide variety of subjects.