# Offline Preference Optimization via Maximum Marginal Likelihood Estimation

arXiv: https://arxiv.org/abs/2510.22881 · HTML: https://mlsanity.com/paper/2510.22881/

## Key facts

- Cited by 1 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 27 of its 45 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [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)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [Implementation Matters in Deep Policy Gradients: A Case Study on PPO and TRPO](https://mlsanity.com/paper/2005.12729/) (2020)
- [Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints](https://mlsanity.com/paper/2309.16240/) (2023)
- [Generalized Preference Optimization: A Unified Approach to Offline Alignment](https://mlsanity.com/paper/2402.05749/) (2024)
- [The Mamba in the Llama: Distilling and Accelerating Hybrid Models](https://mlsanity.com/paper/2408.15237/) (2024)
- [Cal-DPO: Calibrated Direct Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2412.14516/) (2024)
- [From Language to Programs: Bridging Reinforcement Learning and Maximum Marginal Likelihood](https://mlsanity.com/paper/1704.07926/) (2017)
- [RIFF: Learning to Rephrase Inputs for Few-shot Fine-tuning of Language Models](https://mlsanity.com/paper/2403.02271/) (2024)

## Built on by (most cited first, 1 of 1)

- [Beyond Pairs: Your Language Model is Secretly Optimizing a Preference Graph](https://mlsanity.com/paper/2605.08037/) (2026)

## Abstract (arXiv)

Aligning Large Language Models (LLMs) with human preferences is crucial, but standard methods like Reinforcement Learning from Human Feedback (RLHF) are often complex and unstable. In this work, we propose a new, simpler approach that recasts alignment through the lens of Maximum Marginal Likelihood (MML) estimation. Our new MML based Preference Optimization (MMPO) maximizes the marginal log-likelihood of a preferred text output, using the preference pair as samples for approximation, and forgoes the need for both an explicit reward model and entropy maximization. We theoretically demonstrate that MMPO implicitly performs preference optimization, producing a weighted gradient that naturally up-weights chosen responses over rejected ones. Across models ranging from 135M to 8B parameters, we empirically show that MMPO: 1) is more stable with respect to the hyperparameter β compared to alternative baselines, and 2) achieves competitive or superior preference alignment while better preserving the base model's general language capabilities. Through a series of ablation experiments, we show that this improved performance is indeed attributable to MMPO's implicit preference optimization within the gradient updates.