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Despite the significant progress of deep reinforcement learning (RL) in solving sequential decision making problems, RL agents often overfit to training environments and struggle to adapt to new, unseen environments. This prevents robust applications of RL in real world situations, where system dynamics may deviate wildly from the training settings. In this work, our primary contribution is to propose an information theoretic regularization objective and an annealing-based optimization method to achieve better generalization ability in RL agents. We demonstrate the extreme generalization benefits of our approach in different domains ranging from maze navigation to robotic tasks; for the first time, we show that agents can generalize to test parameters more than 10 standard deviations away from the training parameter distribution. This work provides a principled way to improve generalization in RL by gradually removing information that is redundant for task-solving; it opens doors for the systematic study of generalization from training to extremely different testing settings, focusing on the established connections between information theory and machine learning.