# Iterative Nash Policy Optimization: Aligning LLMs with General Preferences via No-Regret Learning

arXiv: https://arxiv.org/abs/2407.00617 · HTML: https://mlsanity.com/paper/2407.00617/

## Key facts

- Cited by 45 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 45 of its 58 references that are in the map.
- First posted on arXiv 30 Jun 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 45)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [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)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [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)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [Nash Learning from Human Feedback](https://mlsanity.com/paper/2312.00886/) (2023)
- [Optimization, Learning, and Games with Predictable Sequences](https://mlsanity.com/paper/1311.1869/) (2013)
- [ReMax: A Simple, Effective, and Efficient Reinforcement Learning Method for Aligning Large Language Models](https://mlsanity.com/paper/2310.10505/) (2023)
- [Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences](https://mlsanity.com/paper/2404.03715/) (2024)
- [Fast Convergence of Regularized Learning in Games](https://mlsanity.com/paper/1507.00407/) (2015)
- [RL with KL penalties is better viewed as Bayesian inference](https://mlsanity.com/paper/2205.11275/) (2022)
- [V-Learning -- A Simple, Efficient, Decentralized Algorithm for Multiagent RL](https://mlsanity.com/paper/2110.14555/) (2021)

## Built on by (most cited first, 30 of 45)

- [Building Math Agents with Multi-Turn Iterative Preference Learning](https://mlsanity.com/paper/2409.02392/) (2024)
- [Agentic Reinforcement Learning with Implicit Step Rewards](https://mlsanity.com/paper/2509.19199/) (2025)
- [Improving Sampling Efficiency in RLVR through Adaptive Rollout and Response Reuse](https://mlsanity.com/paper/2509.25808/) (2025)
- [Improving LLM General Preference Alignment via Optimistic Online Mirror Descent](https://mlsanity.com/paper/2502.16852/) (2025)
- [Enhancing Multi-Step Reasoning Abilities of Language Models through Direct Q-Function Optimization](https://mlsanity.com/paper/2410.09302/) (2024)
- [Demystifying Group Relative Policy Optimization: Its Policy Gradient is a U-Statistic](https://mlsanity.com/paper/2603.01162/) (2026)
- [Magnetic Preference Optimization: Achieving Last-iterate Convergence for Language Model Alignment](https://mlsanity.com/paper/2410.16714/) (2024)
- [Game Theory Meets Large Language Models: A Systematic Survey with Taxonomy and New Frontiers](https://mlsanity.com/paper/2502.09053/) (2025)
- [Extragradient Preference Optimization (EGPO): Beyond Last-Iterate Convergence for Nash Learning from Human Feedback](https://mlsanity.com/paper/2503.08942/) (2025)
- [MaPPO: Maximum a Posteriori Preference Optimization with Prior Knowledge](https://mlsanity.com/paper/2507.21183/) (2025)
- [Robust Reinforcement Learning from Human Feedback for Large Language Models Fine-Tuning](https://mlsanity.com/paper/2504.03784/) (2025)
- [Doubly Robust Alignment for Large Language Models](https://mlsanity.com/paper/2506.01183/) (2025)
- [Greedy Sampling Is Provably Efficient for RLHF](https://mlsanity.com/paper/2510.24700/) (2025)
- [Stackelberg Self-Annotation: A Robust Approach to Data-Efficient LLM Alignment](https://mlsanity.com/paper/2502.18099/) (2025)
- [Stackelberg Learning from Human Feedback: Preference Optimization as a Sequential Game](https://mlsanity.com/paper/2512.16626/) (2025)
- [Beyond Pessimism: Offline Learning in KL-regularized Games](https://mlsanity.com/paper/2604.06738/) (2026)
- [Bridging SFT and DPO for Diffusion Model Alignment with Self-Sampling Preference Optimization](https://mlsanity.com/paper/2410.05255/) (2024)
- [Faster WIND: Accelerating Iterative Best-of-N Distillation for LLM Alignment](https://mlsanity.com/paper/2410.20727/) (2024)
- [COMAL: A Convergent Meta-Algorithm for Aligning LLMs with General Preferences](https://mlsanity.com/paper/2410.23223/) (2024)
- [Multiplayer Nash Preference Optimization](https://mlsanity.com/paper/2509.23102/) (2025)
- [Rethinking Importance Sampling in LLM Policy Optimization: A Cumulative Token Perspective](https://mlsanity.com/paper/2605.07331/) (2026)
- [Pre-DPO: Improving Data Utilization in Direct Preference Optimization Using a Guiding Reference Model](https://mlsanity.com/paper/2504.15843/) (2025)
- [Offline Two-Player Zero-Sum Markov Games with KL Regularization](https://mlsanity.com/paper/2605.13025/) (2026)
- [Best Policy Learning from Trajectory Preference Feedback](https://mlsanity.com/paper/2501.18873/) (2025)
- [RSPO: Regularized Self-Play Alignment of Large Language Models](https://mlsanity.com/paper/2503.00030/) (2025)
- [Pessimism-Free Offline Learning in General-Sum Games via KL Regularization](https://mlsanity.com/paper/2605.00264/) (2026)
- [Sign-SZPO: Provable Preference-based Reinforcement Learning with an Unknown Link Function](https://mlsanity.com/paper/2506.03066/) (2025)
- [Multi-Step Alignment as Markov Games: An Optimistic Online Gradient Descent Approach with Convergence Guarantees](https://mlsanity.com/paper/2502.12678/) (2025)
- [Reward Shaping for (Inference-Time) Alignment: A Stackelberg Game Perspective](https://mlsanity.com/paper/2602.02572/) (2026)
- [Your Self-Play Algorithm is Secretly an Adversarial Imitator: Understanding LLM Self-Play through the Lens of Imitation Learning](https://mlsanity.com/paper/2602.01357/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Human Feedback (RLHF) has achieved great success in aligning large language models (LLMs) with human preferences. Prevalent RLHF approaches are reward-based, following the Bradley-Terry (BT) model assumption, which may not fully capture the complexity of human preferences. In this paper, we explore RLHF under a general preference framework and approach it from a game-theoretic perspective. Specifically, we formulate the problem as a two-player game and propose a novel online algorithm, iterative Nash policy optimization (INPO). The key idea is to let the policy play against itself via no-regret learning, thereby approximating the Nash policy. Unlike previous methods, INPO bypasses the need for estimating the expected win rate for individual responses, which typically incurs high computational or annotation costs. Instead, we introduce a new loss objective that is directly minimized over a preference dataset. We provide theoretical analysis for our approach and demonstrate its effectiveness through experiments on various representative benchmarks. With an LLaMA-3-8B-based SFT model, INPO achieves a 42.6% length-controlled win rate on AlpacaEval 2.0 and a 37.8% win rate on Arena-Hard, showing substantial improvement over the state-of-the-art online RLHF algorithms.