# Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons

arXiv: https://arxiv.org/abs/2301.11270 · HTML: https://mlsanity.com/paper/2301.11270/

## Key facts

- Cited by 247 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 53 of its 103 references that are in the map.
- First posted on arXiv 26 Jan 2023.

## 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 53)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (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)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Red Teaming Language Models to Reduce Harms: Methods, Scaling Behaviors, and Lessons Learned](https://mlsanity.com/paper/2209.07858/) (2022)
- [Improving alignment of dialogue agents via targeted human judgements](https://mlsanity.com/paper/2209.14375/) (2022)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Teaching language models to support answers with verified quotes](https://mlsanity.com/paper/2203.11147/) (2022)
- [Recursively Summarizing Books with Human Feedback](https://mlsanity.com/paper/2109.10862/) (2021)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [Extrapolating Beyond Suboptimal Demonstrations via Inverse Reinforcement Learning from Observations](https://mlsanity.com/paper/1904.06387/) (2019)
- [Is Reinforcement Learning (Not) for Natural Language Processing: Benchmarks, Baselines, and Building Blocks for Natural Language Policy Optimization](https://mlsanity.com/paper/2210.01241/) (2022)
- [Interactive Learning from Policy-Dependent Human Feedback](https://mlsanity.com/paper/1701.06049/) (2017)
- [Policy Finetuning: Bridging Sample-Efficient Offline and Online Reinforcement Learning](https://mlsanity.com/paper/2106.04895/) (2021)
- [Deep TAMER: Interactive Agent Shaping in High-Dimensional State Spaces](https://mlsanity.com/paper/1709.10163/) (2017)
- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Adversarially Trained Actor Critic for Offline Reinforcement Learning](https://mlsanity.com/paper/2202.02446/) (2022)
- [Provable Benefits of Actor-Critic Methods for Offline Reinforcement Learning](https://mlsanity.com/paper/2108.08812/) (2021)
- [Dueling RL: Reinforcement Learning with Trajectory Preferences](https://mlsanity.com/paper/2111.04850/) (2021)
- [Best-Arm Identification in Linear Bandits](https://mlsanity.com/paper/1409.6110/) (2014)
- [Human-in-the-loop: Provably Efficient Preference-based Reinforcement Learning with General Function Approximation](https://mlsanity.com/paper/2205.11140/) (2022)

## Built on by (most cited first, 30 of 247)

- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [Preference Ranking Optimization for Human Alignment](https://mlsanity.com/paper/2306.17492/) (2023)
- [Large Language Model Alignment: A Survey](https://mlsanity.com/paper/2309.15025/) (2023)
- [MEM1: Learning to Synergize Memory and Reasoning for Efficient Long-Horizon Agents](https://mlsanity.com/paper/2506.15841/) (2025)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [A Comprehensive Survey of AI-Generated Content (AIGC): A History of Generative AI from GAN to ChatGPT](https://mlsanity.com/paper/2303.04226/) (2023)
- [ReMax: A Simple, Effective, and Efficient Reinforcement Learning Method for Aligning Large Language Models](https://mlsanity.com/paper/2310.10505/) (2023)
- [Mitigating the Alignment Tax of RLHF](https://mlsanity.com/paper/2309.06256/) (2023)
- [Text2Reward: Reward Shaping with Language Models for Reinforcement Learning](https://mlsanity.com/paper/2309.11489/) (2023)
- [The PRISM Alignment Dataset: What Participatory, Representative and Individualised Human Feedback Reveals About the Subjective and Multicultural Alignment of Large Language Models](https://mlsanity.com/paper/2404.16019/) (2024)
- [Provably Robust DPO: Aligning Language Models with Noisy Feedback](https://mlsanity.com/paper/2403.00409/) (2024)
- [Distributional Preference Learning: Understanding and Accounting for Hidden Context in RLHF](https://mlsanity.com/paper/2312.08358/) (2023)
- [Personalized Language Modeling from Personalized Human Feedback](https://mlsanity.com/paper/2402.05133/) (2024)
- [DPO Meets PPO: Reinforced Token Optimization for RLHF](https://mlsanity.com/paper/2404.18922/) (2024)
- [Explainable Artificial Intelligence (XAI) 2.0: A Manifesto of Open Challenges and Interdisciplinary Research Directions](https://mlsanity.com/paper/2310.19775/) (2023)
- [Provably Mitigating Overoptimization in RLHF: Your SFT Loss is Implicitly an Adversarial Regularizer](https://mlsanity.com/paper/2405.16436/) (2024)
- [Exploratory Preference Optimization: Harnessing Implicit Q*-Approximation for Sample-Efficient RLHF](https://mlsanity.com/paper/2405.21046/) (2024)
- [Critique-out-Loud Reward Models](https://mlsanity.com/paper/2408.11791/) (2024)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [Is RLHF More Difficult than Standard RL?](https://mlsanity.com/paper/2306.14111/) (2023)
- [RLHF Deciphered: A Critical Analysis of Reinforcement Learning from Human Feedback for LLMs](https://mlsanity.com/paper/2404.08555/) (2024)
- [MAPoRL: Multi-Agent Post-Co-Training for Collaborative Large Language Models with Reinforcement Learning](https://mlsanity.com/paper/2502.18439/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [RLHF from Heterogeneous Feedback via Personalization and Preference Aggregation](https://mlsanity.com/paper/2405.00254/) (2024)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [Value-Incentivized Preference Optimization: A Unified Approach to Online and Offline RLHF](https://mlsanity.com/paper/2405.19320/) (2024)
- [Reinforcement Learning with Human Feedback: Learning Dynamic Choices via Pessimism](https://mlsanity.com/paper/2305.18438/) (2023)
- [REBEL: Reinforcement Learning via Regressing Relative Rewards](https://mlsanity.com/paper/2404.16767/) (2024)
- [Robust Preference Optimization through Reward Model Distillation](https://mlsanity.com/paper/2405.19316/) (2024)

## Abstract (arXiv)

We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). Our analysis shows that when the true reward function is linear, the widely used maximum likelihood estimator (MLE) converges under both the Bradley-Terry-Luce (BTL) model and the Plackett-Luce (PL) model. However, we show that when training a policy based on the learned reward model, MLE fails while a pessimistic MLE provides policies with improved performance under certain coverage assumptions. Additionally, we demonstrate that under the PL model, the true MLE and an alternative MLE that splits the K-wise comparison into pairwise comparisons both converge. Moreover, the true MLE is asymptotically more efficient. Our results validate the empirical success of existing RLHF algorithms in InstructGPT and provide new insights for algorithm design. Furthermore, our results unify the problem of RLHF and max-entropy Inverse Reinforcement Learning (IRL), and provide the first sample complexity bound for max-entropy IRL.