# BoNBoN Alignment for Large Language Models and the Sweetness of Best-of-n Sampling

arXiv: https://arxiv.org/abs/2406.00832 · HTML: https://mlsanity.com/paper/2406.00832/

## Key facts

- Cited by 121 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 33 of its 43 references that are in the map.
- First posted on arXiv 2 Jun 2024.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 30 of 33)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [SLiC-HF: Sequence Likelihood Calibration with Human Feedback](https://mlsanity.com/paper/2305.10425/) (2023)
- [Contrastive Preference Optimization: Pushing the Boundaries of LLM Performance in Machine Translation](https://mlsanity.com/paper/2401.08417/) (2024)
- [FUDGE: Controlled Text Generation With Future Discriminators](https://mlsanity.com/paper/2104.05218/) (2021)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)
- [A Survey of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2312.14925/) (2023)
- [Large Language Model Alignment: A Survey](https://mlsanity.com/paper/2309.15025/) (2023)
- [Secrets of RLHF in Large Language Models Part I: PPO](https://mlsanity.com/paper/2307.04964/) (2023)
- [Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking](https://mlsanity.com/paper/2312.09244/) (2023)
- [Disentangling Length from Quality in Direct Preference Optimization](https://mlsanity.com/paper/2403.19159/) (2024)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [Controlled Decoding from Language Models](https://mlsanity.com/paper/2310.17022/) (2023)
- [Theoretical guarantees on the best-of-n alignment policy](https://mlsanity.com/paper/2401.01879/) (2024)
- [Understanding the performance gap between online and offline alignment algorithms](https://mlsanity.com/paper/2405.08448/) (2024)

## Built on by (most cited first, 30 of 121)

- [Fast Best-of-N Decoding via Speculative Rejection](https://mlsanity.com/paper/2410.20290/) (2024)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment](https://mlsanity.com/paper/2503.21878/) (2025)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)
- [BOND: Aligning LLMs with Best-of-N Distillation](https://mlsanity.com/paper/2407.14622/) (2024)
- [RRM: Robust Reward Model Training Mitigates Reward Hacking](https://mlsanity.com/paper/2409.13156/) (2024)
- [Revisiting the Test-Time Scaling of o1-like Models: Do they Truly Possess Test-Time Scaling Capabilities?](https://mlsanity.com/paper/2502.12215/) (2025)
- [Unintentional Unalignment: Likelihood Displacement in Direct Preference Optimization](https://mlsanity.com/paper/2410.08847/) (2024)
- [BEST-Route: Adaptive LLM Routing with Test-Time Optimal Compute](https://mlsanity.com/paper/2506.22716/) (2025)
- [Building Math Agents with Multi-Turn Iterative Preference Learning](https://mlsanity.com/paper/2409.02392/) (2024)
- [VideoChat-R1.5: Visual Test-Time Scaling to Reinforce Multimodal Reasoning by Iterative Perception](https://mlsanity.com/paper/2509.21100/) (2025)
- [Sampling-Efficient Test-Time Scaling: Self-Estimating the Best-of-N Sampling in Early Decoding](https://mlsanity.com/paper/2503.01422/) (2025)
- [RMB: Comprehensively Benchmarking Reward Models in LLM Alignment](https://mlsanity.com/paper/2410.09893/) (2024)
- [TreeBoN: Enhancing Inference-Time Alignment with Speculative Tree-Search and Best-of-N Sampling](https://mlsanity.com/paper/2410.16033/) (2024)
- [Rethinking Mixture-of-Agents: Is Mixing Different Large Language Models Beneficial?](https://mlsanity.com/paper/2502.00674/) (2025)
- [Chasing the Tail: Effective Rubric-based Reward Modeling for Large Language Model Post-Training](https://mlsanity.com/paper/2509.21500/) (2025)
- [Exploring the Limit of Outcome Reward for Learning Mathematical Reasoning](https://mlsanity.com/paper/2502.06781/) (2025)
- [Variational Best-of-N Alignment](https://mlsanity.com/paper/2407.06057/) (2024)
- [Scaling of Search and Learning: A Roadmap to Reproduce o1 from Reinforcement Learning Perspective](https://mlsanity.com/paper/2412.14135/) (2024)
- [MindJourney: Test-Time Scaling with World Models for Spatial Reasoning](https://mlsanity.com/paper/2507.12508/) (2025)
- [From Lists to Emojis: How Format Bias Affects Model Alignment](https://mlsanity.com/paper/2409.11704/) (2024)
- [Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlo](https://mlsanity.com/paper/2504.13139/) (2025)
- [PonderLM: Pretraining Language Models to Ponder in Continuous Space](https://mlsanity.com/paper/2505.20674/) (2025)
- [A Survey of Test-Time Compute: From Intuitive Inference to Deliberate Reasoning](https://mlsanity.com/paper/2501.02497/) (2025)
- [Evaluation of Best-of-N Sampling Strategies for Language Model Alignment](https://mlsanity.com/paper/2502.12668/) (2025)
- [A Survey of Direct Preference Optimization](https://mlsanity.com/paper/2503.11701/) (2025)
- [InfAlign: Inference-aware language model alignment](https://mlsanity.com/paper/2412.19792/) (2024)
- [Inference-Time Reward Hacking in Large Language Models](https://mlsanity.com/paper/2506.19248/) (2025)
- [Sharp Analysis for KL-Regularized Contextual Bandits and RLHF](https://mlsanity.com/paper/2411.04625/) (2024)
- [Soft Best-of-n Sampling for Model Alignment](https://mlsanity.com/paper/2505.03156/) (2025)

## Abstract (arXiv)

This paper concerns the problem of aligning samples from large language models to human preferences using best-of-n sampling, where we draw n samples, rank them, and return the best one. We consider two fundamental problems. First: what is the relationship between best-of-n and approaches to alignment that train LLMs to output samples with a high expected reward (e.g., RLHF or DPO)? To answer this, we embed both the best-of-n distribution and the sampling distributions learned by alignment procedures in a common class of tiltings of the base LLM distribution. We then show that, within this class, best-of-n is essentially optimal in terms of the trade-off between win-rate against the base model vs KL distance from the base model. That is, best-of-n is the best choice of alignment distribution if the goal is to maximize win rate. However, best-of-n requires drawing n samples for each inference, a substantial cost. To avoid this, the second problem we consider is how to fine-tune a LLM to mimic the best-of-n sampling distribution. We derive BoNBoN Alignment to achieve this by exploiting the special structure of the best-of-n distribution. Experiments show that BoNBoN alignment yields substantial improvements in producing a model that is preferred to the base policy while minimally affecting off-target aspects.