In this paper, we survey recent advances in Reinforcement Learning (RL) for
reasoning with Large Language Models (LLMs). RL has achieved remarkable success
in advancing the frontier of LLM capabilities, particularly in addressing
complex logical tasks such as mathematics and coding. As a result, RL has
emerged as a foundational methodology for transforming LLMs into LRMs. With the
rapid progress of the field, further scaling of RL for LRMs now faces
foundational challenges not only in computational resources but also in
algorithm design, training data, and infrastructure. To this end, it is timely
to revisit the development of this domain, reassess its trajectory, and explore
strategies to enhance the scalability of RL toward Artificial SuperIntelligence
(ASI). In particular, we examine research applying RL to LLMs and LRMs for
reasoning abilities, especially since the release of DeepSeek-R1, including
foundational components, core problems, training resources, and downstream
applications, to identify future opportunities and directions for this rapidly
evolving area. We hope this review will promote future research on RL for
broader reasoning models. Github:
https://github.com/TsinghuaC3I/Awesome-RL-for-LRMs