# Shapley-based Data Valuation for LLM Alignment via Sequential Preference Optimization

arXiv: https://arxiv.org/abs/2512.15765 · HTML: https://mlsanity.com/paper/2512.15765/

## 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 44 of its 56 references that are in the map.
- First posted on arXiv 12 Dec 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, 30 of 44)

- [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)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [SLiC-HF: Sequence Likelihood Calibration with Human Feedback](https://mlsanity.com/paper/2305.10425/) (2023)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Skywork-Reward-V2: Scaling Preference Data Curation via Human-AI Synergy](https://mlsanity.com/paper/2507.01352/) (2025)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [Rewards-in-Context: Multi-objective Alignment of Foundation Models with Dynamic Preference Adjustment](https://mlsanity.com/paper/2402.10207/) (2024)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019)
- [Scaling Laws for Reward Model Overoptimization in Direct Alignment Algorithms](https://mlsanity.com/paper/2406.02900/) (2024)
- [Regularizing Hidden States Enables Learning Generalizable Reward Model for LLMs](https://mlsanity.com/paper/2406.10216/) (2024)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [Sequence Tutor: Conservative Fine-Tuning of Sequence Generation Models with KL-control](https://mlsanity.com/paper/1611.02796/) (2016)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [A Marketplace for Data: An Algorithmic Solution](https://mlsanity.com/paper/1805.08125/) (2018)

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

- [ShapE-GRPO: Shapley-Enhanced Reward Allocation for Multi-Candidate LLM Training](https://mlsanity.com/paper/2603.29871/) (2026)

## Abstract (arXiv)

Data valuation is a natural framework for understanding which data sources matter most when aligning a Large Language Model (LLM) from multiple sources. The standard game-theoretic approach treats each source, or equivalently each preference dataset, as a player in a cooperative game and assigns it a contribution score through the Shapley value. In practice, however, Shapley-based valuation is computationally prohibitive because it requires aligning a separate model for every possible coalition of sources, i.e., an exponential number of alignments. We address this challenge for Direct Alignment Algorithms (DAAs), including IPO, which learn through log-policy ratios with respect to a reference policy. We show that, when a model is aligned sequentially source by source, exact optimization makes each stage contribute additively to the log-probability of a full response, up to a prompt-dependent normalization constant. This allows the log-probability assigned by any coalition to a fixed response to be reconstructed from the base policy and the policies trained on each source individually. This reduces the alignment cost of Shapley-based valuation from exponential to linear, since only one model per source needs to be trained to evaluate coalition scores. We test whether this theoretical property remains approximately valid under finite training across several base models and real-world data sources. We finally compute the Shapley values of these sources under multiple reward models, showing how their estimated contributions vary across evaluation criteria.