A common technique to improve learning performance in deep reinforcement learning (DRL) and many other machine learning algorithms is to run multiple learning agents in parallel. A neglected component in the development of these algorithms has been how best to arrange the learning agents involved to improve distributed search. Here we draw upon results from the networked optimization literatures suggesting that arranging learning agents in communication networks other than fully connected topologies (the implicit way agents are commonly arranged in) can improve learning. We explore the relative performance of four popular families of graphs and observe that one such family (Erdos-Renyi random graphs) empirically outperforms the de facto fully-connected communication topology across several DRL benchmark tasks. Additionally, we observe that 1000 learning agents arranged in an Erdos-Renyi graph can perform as well as 3000 agents arranged in the standard fully-connected topology, showing the large learning improvement possible when carefully designing the topology over which agents communicate. We complement these empirical results with a theoretical investigation of why our alternate topologies perform better. Overall, our work suggests that distributed machine learning algorithms could be made more effective if the communication topology between learning agents was optimized.