mlsanityData to 7 Oct 2026

Multi-Step Alignment as Markov Games: An Optimistic Online Gradient Descent Approach with Convergence Guarantees

arXiv 2502.12678 ↗First posted 18 Feb 2025cs.LG cs.AI cs.CLcited by 3

On the map: LLM alignment / RLHF / preference optimisation → Reward modeling and RLHF

Abstract (arXiv)

Reinforcement Learning from Human Feedback (RLHF) has been highly successful in aligning large language models with human preferences. While prevalent methods like DPO have demonstrated strong performance, they frame interactions with the language model as a bandit problem, which limits their applicability in real-world scenarios where multi-turn conversations are common. Additionally, DPO relies on the Bradley-Terry model assumption, which does not adequately capture the non-transitive nature of human preferences. In this paper, we address these challenges by modeling the alignment problem as a two-player constant-sum Markov game, where each player seeks to maximize their winning rate against the other across all steps of the conversation. Our approach Optimistic Multi-step Preference Optimization (OMPO) is built upon the optimistic online mirror descent algorithm~citeprakhlin2013online,joulani17a. Theoretically, we provide a rigorous analysis for the convergence of OMPO and show that OMPO requires O(ε-1) policy updates to converge to an ε-approximate Nash equilibrium. We also validate the effectiveness of our method on multi-turn conversations dataset and math reasoning dataset.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation. Builds on 46 of its 73 references that are in the map. First posted on arXiv 18 Feb 2025.

Builds on

46 of 73 references.

Closest ancestors · 13

Same direction, newest first

  1. 2024Magnetic Preference Optimization: Achieving Last-iterate Convergence for Language Model Alignment22 Oct
  2. 2024BOND: Aligning LLMs with Best-of-N Distillation19 Jul
  3. 2024Iterative Nash Policy Optimization: Aligning LLMs with General Preferences via No-Regret Learning30 Jun
  4. 2024Multi-turn Reinforcement Learning from Preference Human Feedback23 May
  5. 2024RLHF Workflow: From Reward Modeling to Online RLHF13 May
  6. 2024Self-Play Preference Optimization for Language Model Alignment1 May
  7. 2024Direct Nash Optimization: Teaching Language Models to Self-Improve with General Preferences4 Apr
  8. 2024A Minimaximalist Approach to Reinforcement Learning from Human Feedback8 Jan
  9. 2023Nash Learning from Human Feedback1 Dec
  10. 2023Is RLHF More Difficult than Standard RL?25 Jun
  11. 2023Direct Preference Optimization: Your Language Model is Secretly a Reward Model29 May
  12. 2022Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback12 Apr
1 more
  1. 2019Fine-Tuning Language Models from Human Preferences18 Sep

Other references · 33

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2023GPT-4 Technical Reportcited by 18,132
  3. 2022Training language models to follow instructions with human feedbackcited by 15,712
  4. 2024The Llama 3 Herd of Modelscited by 14,192
  5. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  6. 2023Judging LLM-as-a-Judge with MT-Bench and Chatbot Arenacited by 8,393
  7. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  8. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 4,993
  9. 2023Mistral 7Bcited by 3,065
  10. 2020Learning to summarize from human feedbackcited by 2,562
  11. 2024SimPO: Simple Preference Optimization with a Reference-Free Rewardcited by 951
  12. 2023A General Theoretical Paradigm to Understand Learning from Human Preferencescited by 906
21 more
  1. 2023MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Modelscited by 724
  2. 2024ORPO: Monolithic Preference Optimization without Reference Modelcited by 556
  3. 2024Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMscited by 265
  4. 2024MT-Bench-101: A Fine-Grained Benchmark for Evaluating Large Language Models in Multi-Turn Dialoguescited by 247
  5. 2024From r to Q^*: Your Language Model is Secretly a Q-Functioncited by 242
  6. 2017A unified view of entropy-regularized Markov decision processescited by 174
  7. 2024Generalized Preference Optimization: A Unified Approach to Offline Alignmentcited by 155
  8. 2024Token-level Direct Preference Optimizationcited by 135
  9. 2015Taming the Noise in Reinforcement Learning via Soft Updatescited by 125
  10. 2021Independent Policy Gradient Methods for Competitive Reinforcement Learningcited by 97
  11. 2021Last-iterate Convergence of Decentralized Optimistic Gradient Descent/Ascent in Infinite-horizon Competitive Markov Gamescited by 66
  12. 2024Augmenting Math Word Problems via Iterative Question Composingcited by 58
  13. 2024GenARM: Reward Guided Generation with Autoregressive Reward Model for Test-time Alignmentcited by 54
  14. 2024TIS-DPO: Token-level Importance Sampling for Direct Preference Optimization With Estimated Weightscited by 42
  15. 2018A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivitycited by 35
  16. 2024Step-Controlled DPO: Leveraging Stepwise Error for Enhanced Mathematical Reasoningcited by 35
  17. 2020Logistic Q-Learningcited by 34
  18. 2020Online learning in MDPs with linear function approximation and bandit feedbackcited by 29
  19. 2022Proximal Point Imitation Learningcited by 25
  20. 2017A Modular Analysis of Adaptive (Non-)Convex Optimization: Optimism, Composite Objectives, and Variational Boundscited by 23
  21. 2023Efficient Rate Optimal Regret for Adversarial Contextual MDPs Using Online Function Approximationcited by 9

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025Improving LLM General Preference Alignment via Optimistic Online Mirror Descentcited by 24
  2. 2025Proximal Point Nash Learning from Human Feedbackcited by 4
  3. 2026Asymptotic Universal Alignment: A New Alignment Framework via Test-Time Scalingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024COMAL: A Convergent Meta-Algorithm for Aligning LLMs with General Preferences
  2. 2024Hybrid Preference Optimization for Alignment: Provably Faster Convergence Rates by Combining Offline Preferences with Online Exploration
  3. 2025Multiplayer Nash Preference Optimization
  4. 2024Accelerated Preference Optimization for Large Language Model Alignment
  5. 2024Human Alignment of Large Language Models through Online Preference Optimisation
  6. 2023Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint
  7. 2023Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints
  8. 2024Self-Play with Adversarial Critic: Provable and Scalable Offline Alignment for Language Models