Learning to Choose or Choosing to Learn: Best-of-N vs. Supervised Fine-Tuning for Bit String Generation

Using the bit string generation problem as a case study, we theoretically compare two standard methods for adapting large language models to new tasks. The first, referred to as supervised fine-tuning, involves training a new next token predictor on good generations. The second method, Best-of-N, trains a reward model to select good responses from a collection generated by an unaltered base model. If the learning setting is realizable, we find that supervised fine-tuning outperforms BoN through a better dependence on the response length in its rate of convergence. If realizability fails, then depending on the failure mode, BoN can enjoy a better rate of convergence in either n or a rate of convergence with better dependence on the response length.

@article{somerstep2025_2505.17288,
  title={ Learning to Choose or Choosing to Learn: Best-of-N vs. Supervised Fine-Tuning for Bit String Generation },
  author={ Seamus Somerstep and Vinod Raman and Unique Subedi and Yuekai Sun },
  journal={arXiv preprint arXiv:2505.17288},
  year={ 2025 }
}