Abstract: Many of the challenges facing today's reinforcement learning (RL) algorithms, such as robustness, generalization, transfer, and computational efficiency are closely related to compression. Prior work has convincingly argued why minimizing information is useful in the supervised learning setting, but standard RL algorithms lack an explicit mechanism for compression. The RL setting is unique because (1) its sequential nature allows an agent to use past information to avoid looking at future observations and (2) the agent can optimize its behavior to prefer states where decision making requires few bits. We take advantage of these properties to propose a method (RPC) for learning simple policies. This method brings together ideas from information bottlenecks, model-based RL, and bits-back coding into a simple and theoretically-justified algorithm. Our method jointly optimizes a latent-space model and policy to be self-consistent, such that the policy avoids states where the model is inaccurate. We demonstrate that our method achieves much tighter compression than prior methods, achieving up to 5$\times$ higher reward than a standard information bottleneck when constrained to use just 0.3 bits per observation. We also demonstrate that our method learns policies that are more robust and generalize better to new tasks.