We consider a system comprising a file library and a network with a server and multiple users equipped with cache memories. The system operates in two phases: a prefetching phase, where users load their caches with parts of contents from the library, and a delivery phase, where users request files from the library and the server needs to send the uncached parts of the requested files to the users. For the case where the users' caches are arbitrarily loaded, we propose an algorithm based on deep reinforcement learning to minimize the delay of delivering requested contents to the users in the delivery phase. Simulation results demonstrate that our proposed deep reinforcement learning agent learns a coded delivery strategy for sending the requests to the users, which slightly outperforms the state-of-the-art performance in terms of delivery delay, while drastically reducing the computational complexity.