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Typical end-to-end formulations for learning robotic navigation involve predicting a small set of steering command actions (e.g., step forward, turn left, turn right, etc.) from images of the current state (e.g., a bird's-eye view of a SLAM reconstruction). Instead, we show that it can be advantageous to learn with dense action representations defined in the same domain as the state. In this work, we present "spatial action maps," in which the set of possible actions is represented by a pixel map (aligned with the input image of the current state), where each pixel represents a local navigational endpoint at the corresponding scene location. Using ConvNets to infer spatial action maps from state images, action predictions are thereby spatially anchored on local visual features in the scene, enabling significantly faster learning of complex behaviors for mobile manipulation tasks with reinforcement learning. In our experiments, we task a robot with pushing objects to a goal location, and find that policies learned with spatial action maps achieve much better performance than traditional alternatives.