Modern astronomical experiments are designed to achieve multiple scientific goals, from studies of galaxy evolution to cosmic acceleration. These goals require data of many different classes of night-sky objects, each of which has a particular set of observational needs. These observational needs are typically in strong competition with one another. This poses a challenging multi-objective optimization problem that remains unsolved. The effectiveness of Reinforcement Learning (RL) as a valuable paradigm for training autonomous systems has been well-demonstrated, and it may provide the basis for self-driving telescopes capable of optimizing the scheduling for astronomy campaigns. Simulated datasets containing examples of interactions between a telescope and a discrete set of sky locations on the celestial sphere can be used to train an RL model to sequentially gather data from these several locations to maximize a cumulative reward as a measure of the quality of the data gathered. We use simulated data to test and compare multiple implementations of a Deep Q-Network (DQN) for the task of optimizing the schedule of observations from the Stone Edge Observatory (SEO). We combine multiple improvements on the DQN and adjustments to the dataset, showing that DQNs can achieve an average reward of 87%+-6% of the maximum achievable reward in each state on the test set. This is the first comparison of offline RL algorithms for a particular astronomical challenge and the first open-source framework for performing such a comparison and assessment task.