Knowledge underpins reasoning. Recent research demonstrates that when relevant knowledge is provided as additional context to commonsense question answering (QA), it can substantially enhance the performance even on top of state-of-the-art. The fundamental challenge is where and how to find such knowledge that is high quality and on point with respect to the question; knowledge retrieved from knowledge bases are incomplete and knowledge generated from language models are inconsistent. We present Rainier, or Reinforced Knowledge Introspector, that learns to generate contextually relevant knowledge in response to given questions. Our approach starts by imitating knowledge generated by GPT-3, then learns to generate its own knowledge via reinforcement learning where rewards are shaped based on the increased performance on the resulting question answering. Rainier demonstrates substantial and consistent performance gains when tested over 9 different commonsense benchmarks: including 5 in-domain benchmarks that are seen during reinforcement learning, as well as 4 out-of-domain benchmarks that are kept unseen. Our work is the first to report that knowledge generated by models that are orders of magnitude smaller than GPT-3, even without direct supervision on the knowledge itself, can exceed the quality of knowledge elicited from GPT-3 for commonsense QA.