We present an approach for training "agile" character control policies, able to produce a wide variety of motor skills from a single reference motion cycle. Our technique builds off of generative adversarial imitation learning (GAIL), with a key novelty of our approach being to provide modification to the observation map in order to improve agility and robustness. Namely, to support more agile behavior, we adjust the value measurements of the training discriminator through relative features - hence the name ReGAIL. Our state observations include both task relevant relative velocities and poses, as well as relative goal deviation information. In addition, to increase robustness of the resulting gaits, servo gains and damping values are included as part of the policy action to let the controller learn how to best combine tension and relaxation during motion. From a policy informed by a single reference motion, our resulting agent is able to maneuver as needed, at runtime, from walking forward to walking backward or sideways, turning and stepping nimbly. We demonstrate our approach for a humanoid and a quadruped, on both flat and sloped terrains, as well as provide ablation studies to validate the design choices of our framework.