# Toward Optimal LLM Alignments Using Two-Player Games

arXiv: https://arxiv.org/abs/2406.10977 · HTML: https://mlsanity.com/paper/2406.10977/

## Key facts

- Cited by 13 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 54 of its 66 references that are in the map.
- First posted on arXiv 16 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 54)

- [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: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [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)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [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)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [LaMDA: Language Models for Dialog Applications](https://mlsanity.com/paper/2201.08239/) (2022)
- [Llama Guard: LLM-based Input-Output Safeguard for Human-AI Conversations](https://mlsanity.com/paper/2312.06674/) (2023)
- [Red Teaming Language Models with Language Models](https://mlsanity.com/paper/2202.03286/) (2022)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [BeaverTails: Towards Improved Safety Alignment of LLM via a Human-Preference Dataset](https://mlsanity.com/paper/2307.04657/) (2023)
- [AutoDAN: Generating Stealthy Jailbreak Prompts on Aligned Large Language Models](https://mlsanity.com/paper/2310.04451/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Red Teaming Language Models to Reduce Harms: Methods, Scaling Behaviors, and Lessons Learned](https://mlsanity.com/paper/2209.07858/) (2022)
- [Aligning AI With Shared Human Values](https://mlsanity.com/paper/2008.02275/) (2020)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [GPTFUZZER: Red Teaming Large Language Models with Auto-Generated Jailbreak Prompts](https://mlsanity.com/paper/2309.10253/) (2023)
- [Texygen: A Benchmarking Platform for Text Generation Models](https://mlsanity.com/paper/1802.01886/) (2018)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [Catastrophic Jailbreak of Open-source LLMs via Exploiting Generation](https://mlsanity.com/paper/2310.06987/) (2023)
- [Detecting Language Model Attacks with Perplexity](https://mlsanity.com/paper/2308.14132/) (2023)

## Built on by (most cited first, 13 of 13)

- [Rethinking Bradley-Terry Models in Preference-Based Reward Modeling: Foundations, Theory, and Alternatives](https://mlsanity.com/paper/2411.04991/) (2024)
- [MTSA: Multi-turn Safety Alignment for LLMs through Multi-round Red-teaming](https://mlsanity.com/paper/2505.17147/) (2025)
- [Scalable Reinforcement Post-Training Beyond Static Human Prompts: Evolving Alignment via Asymmetric Self-Play](https://mlsanity.com/paper/2411.00062/) (2024)
- [MAGIC: A Co-Evolving Attacker-Defender Adversarial Game for Robust LLM Safety](https://mlsanity.com/paper/2602.01539/) (2026)
- [Game Theory Meets Large Language Models: A Systematic Survey with Taxonomy and New Frontiers](https://mlsanity.com/paper/2502.09053/) (2025)
- [Frictional Agent Alignment Framework: Slow Down and Don't Break Things](https://mlsanity.com/paper/2505.19428/) (2025)
- [The Alignment Waltz: Jointly Training Agents to Collaborate for Safety](https://mlsanity.com/paper/2510.08240/) (2025)
- [Improving Rationality in the Reasoning Process of Language Models through Self-playing Game](https://mlsanity.com/paper/2506.22920/) (2025)
- [Just Say What You Want: Only-prompting Self-rewarding Online Preference Optimization](https://mlsanity.com/paper/2409.17534/) (2024)
- [Exploring Weaknesses in Function Call Models via Reinforcement Learning: An Adversarial Data Augmentation Approach](https://mlsanity.com/paper/2601.19122/) (2026)
- [Model-Agnostic Lifelong LLM Safety via Externalized Attack-Defense Co-Evolution](https://mlsanity.com/paper/2605.13411/) (2026)
- [All you need to break LLMs are Black-Box, Adapting, Efficient, Transferable, Harmful, Applicable ... Attacks](https://mlsanity.com/paper/2606.03647/) (2026)
- [AI Alignment through a Game-theoretic Lens: A Survey](https://mlsanity.com/paper/2608.27910/) (2026)

## Abstract (arXiv)

The standard Reinforcement Learning from Human Feedback (RLHF) framework primarily focuses on optimizing the performance of large language models using pre-collected prompts. However, collecting prompts that provide comprehensive coverage is both tedious and challenging, and often fails to include scenarios that LLMs need to improve on the most. In this paper, we investigate alignment through the lens of two-agent games, involving iterative interactions between an adversarial and a defensive agent. The adversarial agent's task at each step is to generate prompts that expose the weakness of the defensive agent. In return, the defensive agent seeks to improve its responses to these newly identified prompts it struggled with, based on feedback from the reward model. We theoretically demonstrate that this iterative reinforcement learning optimization converges to a Nash Equilibrium for the game induced by the agents. Experimental results in safety scenarios demonstrate that learning in such a competitive environment not only fully trains agents but also leads to policies with enhanced generalization capabilities for both adversarial and defensive agents.