# Revisiting the (Sub)Optimality of Best-of-N for Inference-Time Alignment

arXiv: https://arxiv.org/abs/2603.05739 · HTML: https://mlsanity.com/paper/2603.05739/

## Key facts

- Cited by 3 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 16 of its 35 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [PandaLM: An Automatic Evaluation Benchmark for LLM Instruction Tuning Optimization](https://mlsanity.com/paper/2306.05087/) (2023)
- [Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences](https://mlsanity.com/paper/2404.03715/) (2024)
- [Exploratory Preference Optimization: Harnessing Implicit Q*-Approximation for Sample-Efficient RLHF](https://mlsanity.com/paper/2405.21046/) (2024)
- [The Limits of Inference Scaling Through Resampling](https://mlsanity.com/paper/2411.17501/) (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)
- [The Coverage Principle: How Pre-Training Enables Post-Training](https://mlsanity.com/paper/2510.15020/) (2025)
- [Let Me Think! A Long Chain-of-Thought Can Be Worth Exponentially Many Short Ones](https://mlsanity.com/paper/2505.21825/) (2025)

## Built on by (most cited first, 3 of 3)

- [Towards a theory of inference-time alignment with unknown rewards](https://mlsanity.com/paper/2608.15402/) (2026)
- [ExpBoN: Exponential-Noise Best-of-n for Efficient Test-Time LLM Alignment](https://mlsanity.com/paper/2609.21899/) (2026)
- [Efficient Best-of-N policy evaluation for inference-time alignment](https://mlsanity.com/paper/2610.09250/) (2026)

## Abstract (arXiv)

Best-of-N (BoN) sampling is a widely used inference-time alignment method for language models, whereby N candidate responses are sampled from a reference model and the one with the highest predicted reward according to a learned reward model is selected. Despite its widespread practical use, recent theoretical work has suggested that it is statistically suboptimal and vulnerable to reward hacking, the process by which models exploit weaknesses in the learned reward model to achieve high estimated reward without genuinely improving performance. We revisit this question under assumptions that more closely reflect practice than that of prior work. In particular, in contradistinction to earlier analyses that focused on expected true reward, which may not be meaningful in many practical settings, we investigate how inference-time alignment affects the win-rate, a pairwise comparison-based metric more closely aligned with how reward models are trained and evaluated in practice. We demonstrate that, under minimal conditions on the quality of the reference model and learned reward model, properly tuned BoN is both computationally and statistically optimal in achieving high win-rate, partially explaining its widespread practical success. Because BoN remains susceptible to reward-hacking in this setting, we propose a simple and practical variant that provably eliminates reward-hacking while maintaining optimal statistical performance. Finally, we show that prior approaches are provably suboptimal when considering win-rate, highlighting the importance of choosing appropriate objectives when analyzing inference-time alignment methods.