# BOND: Aligning LLMs with Best-of-N Distillation

arXiv: https://arxiv.org/abs/2407.14622 · HTML: https://mlsanity.com/paper/2407.14622/

## Key facts

- Cited by 76 papers in the map (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 48 of its 70 references that are in the map.
- First posted on arXiv 19 Jul 2024.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 30 of 48)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [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)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Don't Give Me the Details, Just the Summary! Topic-Aware Convolutional Neural Networks for Extreme Summarization](https://mlsanity.com/paper/1808.08745/) (2018)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models](https://mlsanity.com/paper/2201.03544/) (2022)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [Direct Language Model Alignment from Online AI Feedback](https://mlsanity.com/paper/2402.04792/) (2024)
- [The Alignment Problem from a Deep Learning Perspective](https://mlsanity.com/paper/2209.00626/) (2022)

## Built on by (most cited first, 30 of 76)

- [Fast Best-of-N Decoding via Speculative Rejection](https://mlsanity.com/paper/2410.20290/) (2024)
- [A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systems](https://mlsanity.com/paper/2504.09037/) (2025)
- [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)
- [Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems](https://mlsanity.com/paper/2505.15201/) (2025)
- [RRM: Robust Reward Model Training Mitigates Reward Hacking](https://mlsanity.com/paper/2409.13156/) (2024)
- [Systematic Evaluation of LLM-as-a-Judge in LLM Alignment Tasks: Explainable Metrics and Diverse Prompt Templates](https://mlsanity.com/paper/2408.13006/) (2024)
- [Self-Generated Critiques Boost Reward Modeling for Language Models](https://mlsanity.com/paper/2411.16646/) (2024)
- [Preserving Diversity in Supervised Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2408.16673/) (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)
- [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)
- [Exploring the Limit of Outcome Reward for Learning Mathematical Reasoning](https://mlsanity.com/paper/2502.06781/) (2025)
- [Scaling of Search and Learning: A Roadmap to Reproduce o1 from Reinforcement Learning Perspective](https://mlsanity.com/paper/2412.14135/) (2024)
- [From Lists to Emojis: How Format Bias Affects Model Alignment](https://mlsanity.com/paper/2409.11704/) (2024)
- [PonderLM: Pretraining Language Models to Ponder in Continuous Space](https://mlsanity.com/paper/2505.20674/) (2025)
- [Teaching Language Models to Critique via Reinforcement Learning](https://mlsanity.com/paper/2502.03492/) (2025)
- [POPE: Learning to Reason on Hard Problems via Privileged On-Policy Exploration](https://mlsanity.com/paper/2601.18779/) (2026)
- [A Survey of Test-Time Compute: From Intuitive Inference to Deliberate Reasoning](https://mlsanity.com/paper/2501.02497/) (2025)
- [Weight Ensembling Improves Reasoning in Language Models](https://mlsanity.com/paper/2504.10478/) (2025)
- [Alignment of Diffusion Models: Fundamentals, Challenges, and Future](https://mlsanity.com/paper/2409.07253/) (2024)
- [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)
- [Soft Best-of-n Sampling for Model Alignment](https://mlsanity.com/paper/2505.03156/) (2025)
- [Exploring Data Scaling Trends and Effects in Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2503.22230/) (2025)
- [AdaptiveStep: Automatically Dividing Reasoning Step through Model Confidence](https://mlsanity.com/paper/2502.13943/) (2025)
- [Policy Filtration for RLHF to Mitigate Noise in Reward Models](https://mlsanity.com/paper/2409.06957/) (2024)
- [Magnetic Preference Optimization: Achieving Last-iterate Convergence for Language Model Alignment](https://mlsanity.com/paper/2410.16714/) (2024)

## Abstract (arXiv)

Reinforcement learning from human feedback (RLHF) is a key driver of quality and safety in state-of-the-art large language models. Yet, a surprisingly simple and strong inference-time strategy is Best-of-N sampling that selects the best generation among N candidates. In this paper, we propose Best-of-N Distillation (BOND), a novel RLHF algorithm that seeks to emulate Best-of-N but without its significant computational overhead at inference time. Specifically, BOND is a distribution matching algorithm that forces the distribution of generations from the policy to get closer to the Best-of-N distribution. We use the Jeffreys divergence (a linear combination of forward and backward KL) to balance between mode-covering and mode-seeking behavior, and derive an iterative formulation that utilizes a moving anchor for efficiency. We demonstrate the effectiveness of our approach and several design choices through experiments on abstractive summarization and Gemma models. Aligning Gemma policies with BOND outperforms other RLHF algorithms by improving results on several benchmarks.