What is the objective of reasoning with reinforcement learning?

Damek Davis, Benjamin Recht
10/15/2025
cs.LGmath.OC

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Abstract

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.

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Cite this paper

@article{davis2025what,
  title  = {What is the objective of reasoning with reinforcement learning?},
  author = {Damek Davis and Benjamin Recht},
  year   = {2025},
  eprint = {2510.13651},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2510.13651v1}
}

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