Research on automated image enhancement has gained momentum in recent years, partially due to the need for easy-to-use tools for enhancing pictures captured by ubiquitous cameras on mobile devices. Many of the existing leading methods employ machine-learning-based techniques, by which some enhancement parameters for a given image are found by relating the image to the training images with known enhancement parameters. While knowing the structure of the parameter space can facilitate search for the optimal solution, none of the existing methods has explicitly modeled and learned that structure. This paper presents an end-to-end, novel joint regression and ranking approach to model the interaction between desired enhancement parameters and images to be processed, employing a Gaussian process (GP). GP allows searching for ideal parameters using only the image features. The model naturally leads to a ranking technique for comparing images in the induced feature space. Comparative evaluation using the ground-truth based on the MIT-Adobe FiveK dataset plus subjective tests on an additional data-set were used to demonstrate the effectiveness of the proposed approach.