With the continued introduction of driverless events to Formula:Society of Automotive Engineers (F:SAE) competitions around the world, teams are investigating all aspects of the autonomous vehicle stack. This paper presents the use of Deep Reinforcement Learning (DRL) and Inverse Reinforcement Learning (IRL) to map locally-observed cone positions to a desired steering angle for race track following. Two state-of-the-art algorithms not previously tested in this context: soft actor critic (SAC) and adversarial inverse reinforcement learning (AIRL), are used to train models in a representative simulation. Three novel reward functions for use by RL algorithms in an autonomous racing context are also discussed. Tests performed in simulation and the real world suggest that both algorithms can successfully train models for local path following. Suggestions for future work are presented to allow these models to scale to a full F:SAE vehicle.