  Reinforcement Learning from Human Feedback (\textbf{RLHF}) has emerged as a
dominant approach for aligning LLM outputs with human preferences. Inspired by
the success of RLHF, we study the performance of multiple algorithms that learn
from feedback (Expert Iteration, Proximal Policy Optimization (\textbf{PPO}),
Return-Conditioned RL) on improving LLM reasoning capabilities. We investigate
both sparse and dense rewards provided to the LLM both heuristically and via a
learned reward model. We additionally start from multiple model sizes and
initializations both with and without supervised fine-tuning (\textbf{SFT})
data. Overall, we find all algorithms perform comparably, with Expert Iteration
performing best in most cases. Surprisingly, we find the sample complexity of
Expert Iteration is similar to that of PPO, requiring at most on the order of
$10^6$ samples to converge from a pretrained checkpoint. We investigate why
this is the case, concluding that during RL training models fail to explore
significantly beyond solutions already produced by SFT models. Additionally, we
discuss a trade off between maj@1 and pass@96 metric performance during SFT
training and how conversely RL training improves both simultaneously. We then
conclude by discussing the implications of our findings for RLHF and the future
role of RL in LLM fine-tuning.
