In this work, we propose a deep reinforcement learning (DRL) based reactive planner to solve large-scale Lidar-based autonomous robot exploration problems in 2D action space. Our DRL-based planner allows the agent to reactively plan its exploration path by making implicit predictions about unknown areas, based on a learned estimation of the underlying transition model of the environment. To this end, our approach relies on learned attention mechanisms for their powerful ability to capture long-term dependencies at different spatial scales to reason about the robot's entire belief over known areas. Our approach relies on ground truth information (i.e., privileged learning) to guide the environment estimation during training, as well as on a graph rarefaction algorithm, which allows models trained in small-scale environments to scale to large-scale ones. Simulation results show that our model exhibits better exploration efficiency (12% in path length, 6% in makespan) and lower planning time (60%) than the state-of-the-art planners in a 130m x 100m benchmark scenario. We also validate our learned model on hardware.