# ShapE-GRPO: Shapley-Enhanced Reward Allocation for Multi-Candidate LLM Training

arXiv: https://arxiv.org/abs/2603.29871 · HTML: https://mlsanity.com/paper/2603.29871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 47 of its 53 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 47)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [DS-1000: A Natural and Reliable Benchmark for Data Science Code Generation](https://mlsanity.com/paper/2211.11501/) (2022)
- [In-context Autoencoder for Context Compression in a Large Language Model](https://mlsanity.com/paper/2307.06945/) (2023)
- [Token-level Direct Preference Optimization](https://mlsanity.com/paper/2404.11999/) (2024)
- [DPO Meets PPO: Reinforced Token Optimization for RLHF](https://mlsanity.com/paper/2404.18922/) (2024)
- [GPT4Rec: A Generative Framework for Personalized Recommendation and User Interests Interpretation](https://mlsanity.com/paper/2304.03879/) (2023)
- [Data Shapley in One Training Run](https://mlsanity.com/paper/2406.11011/) (2024)
- [Dense Reward for Free in Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2402.00782/) (2024)
- [Collaborative Machine Learning with Incentive-Aware Model Rewards](https://mlsanity.com/paper/2010.12797/) (2020)
- [A Systematic Survey of Text Summarization: From Statistical Methods to Large Language Models](https://mlsanity.com/paper/2406.11289/) (2024)
- [TLCR: Token-Level Continuous Reward for Fine-grained Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2407.16574/) (2024)
- [TokenSHAP: Interpreting Large Language Models with Monte Carlo Shapley Value Estimation](https://mlsanity.com/paper/2407.10114/) (2024)

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

- [Many Right Answers, One Training Example: Removing Responder Noise from GRPO for LLM Recommenders](https://mlsanity.com/paper/2610.17771/) (2026)

## Abstract (arXiv)

In user-agent interaction scenarios such as recommendation, brainstorming, and code suggestion, Large Language Models (LLMs) often generate sets of candidate recommendations where the objective is to maximize the collective utility of the entire set rather than individual candidates independently. However, existing reinforcement learning post-training paradigms, such as Group Relative Policy Optimization (GRPO), typically assign the same set-level scalar reward to every candidate in the set. This leads to noisy training signals where poor candidates free-ride on the high reward produced by a single strong peer, resulting in suboptimal exploration. To address this, we propose Shapley-Enhanced GRPO (ShapE-GRPO). By leveraging the permutation-invariant nature of set-level utility, we derive a Shapley-enhanced formulation from cooperative game theory to decompose set-level rewards into granular, candidate-specific signals. We show that our formulation preserves the fundamental axioms of the Shapley value while remaining computationally efficient with polynomial-time complexity. Empirically, ShapE-GRPO consistently outperforms standard GRPO across diverse datasets with accelerated convergence during training.