Reinforcement Learning (RL) can be used to fit a mapping from patient state to a medication regimen. Prior studies have used deterministic and value-based tabular learning to learn a propofol dose from an observed anesthetic state. Deep RL replaces the table with a deep neural network and has been used to learn medication regimens from registry databases. Here we perform the first application of deep RL to closed-loop control of anesthetic dosing in a simulated environment. We use the cross-entropy method to train a deep neural network to map an observed anesthetic state to a probability of infusing a fixed propofol dosage. During testing, we implement a deterministic policy that transforms the probability of infusion to a continuous infusion rate. The model is trained and tested on simulated pharmacokinetic/pharmacodynamic models with randomized parameters to ensure robustness to patient variability. The deep RL agent significantly outperformed a proportional-integral-derivative controller (median absolute performance error 1.7% +/- 0.6 and 3.4% +/- 1.2). Modeling continuous input variables instead of a table affords more robust pattern recognition and utilizes our prior domain knowledge. Deep RL learned a smooth policy with a natural interpretation to data scientists and anesthesia care providers alike.