We show that several popular algorithms for reinforcement learning in large language models with binary rewards can be viewed as stochastic gradient ascent on a monotone transform of the probability of a correct answer given a prompt. In particular, the transformation associated with rejection sampling algorithms is the logarithm and that associated with the GRPO algorithm is the arcsine of the square root.
@article{arxiv.2510.13651,
title = {What is the objective of reasoning with reinforcement learning?},
author = {Damek Davis and Benjamin Recht},
journal= {arXiv preprint arXiv:2510.13651},
year = {2025}
}