Pushing objects through cluttered scenes is a challenging task, especially when the objects to be pushed have initially unknown dynamics and touching other entities has to be avoided to reduce the risk of damage. In this paper, we approach this problem by applying deep reinforcement learning to generate pushing actions for a robotic manipulator acting on a planar surface where objects have to be pushed to goal locations while avoiding other items in the same workspace. With the latent space learned from a depth image of the scene and other observations of the environment, such as contact information between the end effector and the object as well as distance to the goal, our framework is able to learn contact-rich pushing actions that avoid collisions with other objects. As the experimental results with a six degrees of freedom robotic arm show, our system is able to successfully push objects from start to end positions while avoiding nearby objects. Furthermore, we evaluate our learned policy in comparison to a state-of-the-art pushing controller for mobile robots and show that our agent performs better in terms of success rate, collisions with other objects, and continuous object contact in various scenarios.