Davis and Recht: GRPO, rejection sampling share an objective

Reinforcement-learning fine-tuning of large language models, in the binary-reward case, is the same optimizer wearing different hats. That is the claim of a short new arXiv note from Damek Davis and Benjamin Recht.

The abstract, in full: '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.' The transform is what changes between methods. For rejection sampling it is the logarithm; for GRPO, 'the arcsine of the square root.'

The paper is filed under machine learning and optimization, and its public face is those two sentences. It does not report experiments or benchmarks; it offers a mathematical reading of what algorithms already in wide use are doing.